Equations, Graphs and Translations

• Calculator Addition [Anthony, 6/30/1996]
  How does a calculator add?

• Changing a Trigonometric Graph [Wang, 08/06/1998]
  How do you graph: -cos 2x / 2?

• Converting and Graphing Coordinates [Echon, 5/28/1996]
  How do you convert a decimal to a polar coordinate and graph it?

• Curve Fitting [Hunsaker, 12/13/1996]
  How do you convert points on a graph to a line?

• Equations of a Line given Two Points [Malvern, 8/31/1996]
  How do you find the equation of a line going through two points if you only know the two points?

• Finding y-intercepts [Ourpond, 6/12/1996]
  I'm having a problem with finding and graphing y-intercepts of linear equations.

• Formula for Point in Rectangle [Scott, 5/31/1996]
  I need a formula that will allow me to determine whether or not a specified point lies within a rectangle.

• Graphing Coordinates [Gallagher, 1/15/1997]
  How can you tell if you have a straight line just by looking at the numbers?

• Graphing y = mx+b [Sturman, 6/28/1996]
  I don't understand what y = mx+b means and how to do slope intercept form.

• An Introduction to Parabolas [Hayley, 02/04/1999]
  What is a parabola? What are some of its properties? What are some examples of parabolas in real life?

• Non-Algebraic Explanation of a Parabola [Donelle, 05/16/2000]
  What does a parabola look like? How is it formed?

• Rational Inequality [Alan, 10/09/2001]
  Solve this rational inequality and give an answer in interval notation: -5/(3h+2) greater than or equal to 5/h.

• Simplify this equation: (x+y)/(y^2-xy-y+x) + (y+1)/(xy-x-y+1) + (x+1)/(x^2-xy-x+y) [al665009, 8/18/1995]
  A rare '"live" talk session with Dr. Math about factoring an equation.

• Stem-and-leaf Graph or Stemplot [Laurain, 10/12/1997]
  Can you explain a stem leaf graph?

• Tables, Graphs, and Equations [Chelsea, 09/04/2001]
  Make a table of values to determine the coordinates of three points that lie on the graph of y = 3x+5. Use the headings x, 3x = 5,y, and (x,y). Then...

• Translating Parabolas and Completing the Square [Jason, 5/23/1995]
  The subject is parabolas translated from the origin and standard equations. State the coordinates of the vertex, and sketch the graph of the following: y^2+8y+8x-8=0.

• When is a Slope 0 or Undefined? [Purple, 3/29/1997]
  How do I know when the slope of an equation is zero or undefined (no slope)?

• Working with Two Equations using Graphs [Brenda, 01/16/2002]
  You estimate that you can make muffins for $.30 each. Advertising will cost $18.00. You sell the muffins for $.75 each. Write and graph equations to represent income and expenses. Find the break-even point.

• Graphing a Parabola [cornfed9, 4/3/1995]
  How do you graph the quadratic equation, y=3(x+1)^2 -20?

• Parabola Equation [Jason, 5/15/1995]
  I'm trying to learn equations of parabolas. The example given is: find the equation of the parabola with vertex (0,0) and focus (0,-3)...

• Equation of a Sphere [Crist, 7/3/1995]
  What is the equation for a sphere on a graph with the dimensions x, y, and z?

• Point Contained by a Circle [Hartlen, 8/8/1995]
  How can I tell if an arbitrary point on a plane is contained by a circle?

• Drawing Spirals on Your Computer [Bailey, 9/5/1995]
  I want to draw spirals with the computer. I don't know how. Could you send me formula(s) I can use to do it?

• The Equation of a Cone [Crespo, 9/13/1995]
  I would like to know the equation of a cone. Could you help me?

• Finding the Equations of Two Circles [Badar, 9/30/1995]
  Find the equation of the circles with the center at (4,-7) and touching (externally and internally) the circle with the equation: (X^2)+(Y^2)+4X-2Y+1=0.

• More Questions on Finding the Equation of a Circle [Badar, 10/1/1995]
  Find the equation of the circle containing the points (-1, -2) and (6,-1) and touching the x-axis.

• Using Descartes' Method of Tangents [Dinsmorm, 10/2/1995]
  Given a point P(3,9) on a parabola y=x^2, how do I find the slope of the tangent to the parabola at point P using Descartes' method of tangents?

• Equation for an Ellipse [Jensen, 10/27/1995]
  I found the right formula for a circle but can't find it for an ellipse.

• Graphing and Understanding Conic Equations [McIlwain, 12/11/1995]
  How can I sketch and find the vertices of this conic equation?

• Similar Graphs [Feger, 12/11/1995]
  How would you describe how the two graphs of y = one over the square root of x squared and y = one over the square root of x squared minus 4 are similar and dissimilar?

• Quintic Equations [Davis, 1/27/1996]
  What does Quintic mean?

• Describing the Graph of an Equation [Khanna, 1/27/1996]
  Which of the following is true of the graph of the equation: y = 2x^2 - 5x + 3 ?...

• Practical Uses for Computing Parabolas [Indon, 1/30/1996]
  Could you give me three practical uses for computing parabolas and tell me the significance of computing the parabola in regard to its application?

• Composite Functions [Connie, 1/31/1996]
  If f(x) = 3, and g(x) = x^2 + 1 divided by the square root of (x^2 -1), how do you evaluate the composite function of f composed with g (f circle g)?

• Pre-calculus Function Question [Belter, 2/8/1996]
  Does the function f(x)=3De^(1/x) have a local minimum?

• Solving a Fractional Equation [Larrieux, 3/10/1996]
  Can you help me with this? (M+N)/(N-M) + (M^2+N^2)/(N^2-M^2) - (2M)/(M-N) = ?

• Composite Functions [Santoso, 4/5/1996]
  1) fog(x) = 7x + 3; gof(x) = 7x - 3; f(0) = 1; g(0) = .....

• Asymptotes [Moshfeghian, 4/13/1996]
  I have a question about the oblique asymptote of the function: F( X ) = ( X^3 - 3X^2 + 2X - 8 ) / ( X^2 + 4X + 4 )...

• Polar to Rectangular Conversions [Glick, 4/19/1996]
  How do I convert "8 cis 30" into rectangular coordinates?

• Graphing Trigonometry Equations [Smallwood, 5/15/1996]
  How do I graph this one: Sin A - Cos A ?

• Graphing Sin and Cosine Functions [BasuC, 5/24/1996]
  I really need some help in finding the graphs of the following functions...

• Finding a Point on a Circle [Gray, 5/28/1996]
  How do I find the y1 value?

• Graph of Geometric Relations [Fox, 6/1/1996]
  Sketch an appropriate graph to illistrate z^- and z if z is in quadrant 1.

• Inverse Function for Natural Numbers [Tibor, 6/10/1996]
  I've got a question about the function n = 0.5((a+b)^2+3a+b), which is a one-to-one bijection from pairs (a,b) of natural numbers to single natural numbers n.

• Coordinates of a Point [Wong, 6/12/1996]
  ABC is a right-angled triangle labeled counter-clockwise with its point C lying on the line y=3x. A is (2,1) and B is (5,5). Find the two possible coordinates of C.

• Direct and Indirect Variation [Adam, 6/12/1996]
  Please explain direct and indirect variation.

• Sketching Curves [Razzaq, 6/24/1996]
  How do I sketch the curve y = log natural of x/ (1-x)?

• Mapping Points [Trigonix, 6/25/1996]
  How do you map points inside a 4-point convex polygon onto another 4 point convex polygon?

• Big O: 2 Functions Map from N to N+ [Turner, 6/25/1996]
  If f, g: N -> N+, then either f(x) is O(g(x)) or g(x) is O(f(x)). Why?

• Cubic Polynomial [Lanaya, 6/27/1996]
  Show that the graph of every cubic polynomial has a point of symmetry.

• Given n Points, find a Polynomial Function... [Richard, 6/27/1996]
  Find a polynomial F(x) of degree less than n so that the graph of F passes through all of the points.

• Generating Fractal Equations [Tardis, 7/1/1996]
  Is there any way to generate a fractal equation from a set of numbers?

• The Graph of f [Ocastill, 7/3/1996]
  Where are its local and absolute maxima and minima? What are the x-intercepts of the graph of f?...

• Parabola Focal Point [Kaelin, 7/3/1996]
  What are the rules for the focal point of a parabola?

• Finding the Equation of a Line [Alfred, 8/2/1996]
  What is the equation of the line that contains the point (4, -4) and is perpendicular to the line defined by 2x-5y+3 = 0?

• Equation of Parabola with Given Vertex, Point [Everette, 8/4/1996]
  How do I find the equations for all parabolas containing the origin whose vertex is at (2,1)?

• Slope of Lines [emsmdt04, 8/6/1996]
  What is the slope of the line y = -px + 5 if the line goes through (0, -3)? Why does the y-axis have an infinite slope, and the x-axis have a slope of 0?

• About Hyperbolas [Ryuen, 8/7/1996]
  Find the graph and the equation of a hyperbola.

• Finding a Point Equidistant From Two Other Points [Jason, 8/18/1996]
  Point A is (-5,-3), and point B is (-1,-5); to be equidistant from A and B, what should the value of k be for the point (3,k)?

• Is y = abs (x) Continuous? [Hayes, 8/29/1996]
  Is y equals the absolute value of x a continuous function?

• Equation for a Vertical Line [Dhitchens, 8/29/1996]
  What is equation for a vertical line passing through (7, -10)?

• Piece-wise Notation and Absolute Value [Drbama, 9/9/1996]
  How do I use piece-wise notation to write x in terms of y for "y=2x+ abs(2-x)"?

• Units for Inverse Quantity [Mercury, 9/10/1996]
  I have a graph of time vs. 1/distance. What units do I use for 1/ distance - cm^-1?

• Translation [Geramiya, 9/11/1996]
  What does translation mean?

• Domain of a Function [Spoth, 9/13/1996]
  What is the domain of f(x)= x/sqrt(x^2-4)?

• Inverse Function [Dianne, 9/15/1996]
  Given f(x) = 1 - 2/x what is f-1(x) ?

• Lines and t-tables [Anderson, 11/09/1996]
  How do you use t-tables to graph lines?

• Bezier Splines [Deichmeister, 12/03/1996]
  What are the equations for Bezier splines? How would I graph them?

• Finding Equations of Parabolas [Duguay, 12/12/1996]
  Determine the equation of the parabola whose vertex is at (1,3) and whose directrix is y=x.

• Using Graphs to Solve Problems [Gambill, 12/29/1996]
  How do you use graphs to find the answers to questions?

• Graphing Parabolas [Mui, 1/16/1997]
  How do you know how to graph a parabola from looking at its equation?

• Domain/Range of a Function [Jennifer, 1/22/1997]
  How do you find the domain and range of the function f(x) = 2x^2-3x+1? (Both with and without calculus.)

• Parabola Problems [Smith, 2/23/1997]
  A culvert is shaped like a parabola, 18 centimeters across the top and 12 centimeters deep. How wide is the culvert 8 centimeters from the top?

• Definition of a Parabola [Smith, 2/23/1997]
  Suppose that (x, y) is to be on the parabola. Suppose that the line mentioned in the definition is given by x = -p. Find the distance between (x, y) and the line...

• Equation of a Parabola [Croman, 03/04/1997]
  Determine the equation of a parabola given its vertex and either the equation of the directrix or the coordinates of the focus.

• Curve Fitting [Hardinger, 03/08/1997]
  I need help writing an algorithm that fits a curve to a given set of data points.

• Pareto and Bar Charts [King, 3/12/1997]
  What are three distinguishing differences between Pareto Charts and Bar Charts?

• Polar Equation of a Circle [Frank, 4/12/1997]
  Given the polar equations r = a*sin (theta) and r = a*cos (theta), what influence does a have on the graph?

• Graphing Trig Functions [Nem, 05/03/1997]
  How do you graph y = 3sin4x-3?

• Parabola Equations [Williams, 05/12/1997]
  Deriving the standard equation for a parabola from its focus and directrix; manipulating this equation to change the graph's appearance.

• Naming and Graphing Functions [Perfect, 06/16/1997]
  Can you tell me about the different families of functions?

• Formula for a Helix [Mahler, 07/08/1997]
  What is the formula that gives the height above the ground of a point on a helix?

• TV Transmitters [Parsons, 07/22/1997]
  If two TV transmitters are within 150 kilometers of each other, they must be assigned different channels. Construct a graph that shows the given problem and use it to find the number of channels needed.

• Graphing Slanted Lines [Richardson, 07/22/1997]
  When graphing slanted lines what does it mean when the instructions say add, subtract, or divide both sides by a particular number?

• Lagrange Polynomial Interpolation [Wang, 08/08/1997]
  Please give me the definition and a brief example of how it works.

• Graphing Equations [Dot, 08/15/1997]
  I know the coordinates of these equations, but what are the names and how do I graph them?

• Difference Quotient Function [Hogue, 09/06/1997]
  Find the equation of the line tangent to a curve f(x) = x^3 - 7x^2 + 12x + 2 at the point (3,2) without using calculus.

• Solve for Radius [Culpepper, 09/09/1997]
  Given a circle through three points, what is the equation for the intersection of the perpendicular bisectors?

• Types of Linear Systems [Devenell, 10/13/1997]
  What is meant when a type of linear system is said to be a consistent or an inconsistent system?

• Graph Intercepts [Guenther, 11/06/1997]
  How would I find the intercept for a problem such as 3x-2y = 12?

• Graphing an Equation [Loh, 11/08/1997]
  Please explain how to graph this equation: y = a + b(x) + c(x^2) + ...

• Root Multiplicity and Polynomial Functions [Rubinshteyn, 11/16/1997]
  What effect does multiplicity [e.g. (x+1)(x-2)^2 where -1 has a multiplicity of 1 and 2 of 2] have on a polynomial function?

• Decimal to Polar Coordinates [Louis, 11/23/1997]
  I need to know how to convert from rectangular coordinates back to polar.

• Parabola [Jen, 12/23/1997]
  Find the vertex, axis of symmetry, directrix, focus, distance from the vertex to the focus, and the latus rectum.

• Graph the Ellipse... [White, 01/01/1998]
  [((x-1)^2)/2^2] + [((y-2)^2)/2^2] = 1. Graph the ellipse and find the major and minor axes, the foci, the eccentricity, and the center.

• Equation of a Line [Amanda, 01/27/1998]
  How do I find the equation of a line through origin perpendicular to 2x + 3y = 5?

• Connecting the Dots [Freeman, 02/02/1998]
  How do you know whether or not to connect the dots when graphing a real-life function?

• Minimum Distance [Putnam, 02/07/1998]
  What is the minimum possible distance between a point on the graph of x^2+y^2 = 1 and a point on the graph of xy = 1?

• Algorithm for Finding Pi, in C [Yang, 02/14/1998]
  I would like to know how to implement various algorithms for finding pi in the C language.

• Writing a TI-82 Program [Guyer, 02/20/1998]
  How can I write a program that will solve quadratic equations on my TI-82 calculator?

• Determining Tangent to an Ellipse, Minimizing Area [Huesser, 02/20/1998]
  Find the equation of the tangent to the ellipse that forms, with the coordinate axes, the triangle of smallest possible area.

• Degenerate Conics [Kiczek, 03/04/1998]
  Identifying the degenerate cases for the graphs of equations in conic form.

• Lines Partitioning a Plane [Regimbald, 03/09/1998]
  Into how many disjoint regions do n coplanar lines partition the plane?

• Locus of the Midpoint of a Chord [Chew, 03/13/1998]
  Show that the locus of the midpoint of the chord is a hyperbola.

• Equations with Two Variables [Gina, 03/25/1998]
  Identify and find solutions to systems of equations or inequalities by graphing.

• Understanding Parametric Equations [Demergian, 04/02/1998]
  Can you explain the basic principles of parametric equations?

• Perpendicular Distance [Albester, 04/10/1998]
  Prove that the distance from a line ax + by + c = 0 to the point (h,k) is (a*h + b*k + c)/(a^2+b^2)^(1/2).

• Graphing a Circle [Peisch, 04/14/1998]
  I would like to know how to graph the equation of a circle.

• Determining Linear Relations [Missy, 04/22/1998]
  Given a set of points on a plane, how can you tell if the relation between them is linear, quadratic, cubic, or exponential?

• Uses for Parametric Equations [Immerman, 04/23/1998]
  What is a parametric equation used for? Can you give me an example?

• Deriving the Hyperbola Formula [Gauteaux, 04/27/1998]
  When speaking of hyperbolas, why does C^2 = A^2 + B^2?

• Linear and Circular Parametric Equations [Preston, 05/05/1998]
  Using parametric equations to plot a line segment connecting any two points on the plane.

• Parabolic Equation of an Arch [Child, 05/25/1998]
  Finding the equation of the parabola in the McDonald's golden arches.

• Graph of Circle as a Function [Thompson, 05/30/1998]
  The graph of a circle is not a function because it fails the vertical line test. How could you make it a function?

• Graphing Systems Equations [Sifferman, 06/01/1998]
  How do you solve this system of equations by graphing: 3x + 2y = 5 and -3x - 2y = 10?

• Graphing a Function with Asymptotes [Hasan, 07/05/1998]
  How do you find the asymptotes of f(x) = (2x + 1)/(x - 3)? How do you use the asymptotes to graph the function?

• Sketching a Function [MatherWu, 07/06/1998]
  Can you help me piece a function together so that the following hold? It is increasing and concave up on (-infinity, 1) ...

• Finding Asymptotes [Robinson, 07/06/1998]
  In the equation y = (m/x) + c, how do the values of m and c affect the graph? How do you find the asymptotes?

• Direct and Indirect Variation [Sparrow, 07/09/1998]
  Can you explain the difference between direct and indirect variation? How would you interpret them in a word problem?

• Lines Tangent to a Hyperbola [Bryan, 07/14/1998]
  If y = 2x + k is a line tangent to the graph x^2 + y^2 = 1, what is k?

• Graphing Linear Equations [Meagan, 07/14/1998]
  Can you give me a step by step guide to graphing linear equations?

• Parametric Equations [Li, 07/21/1998]
  A curve is given parametrically by the equations: x = (3-2k)^2 and y = (2+k)^2. Find dy/dx, the x-intercept, the cartesian equation...

• Polar Coordinates From Cartesian Coordinates [Cherry, 07/27/1998]
  How do you find the polar coordinates from the Cartesian coordinate (3, -3 sqrt(3))?

• Manipulating Roots [Wave, 08/08/1998]
  If a and b are the roots of the equation 3x^2 - 5x + 1 = 0, find the equation whose roots are a/b and b/a.

• Equations in Intercept Form [Cole, 08/27/1998]
  Show that an equation for a line with nonzero x- and y-intercepts can be written as x/a + y/b = 1...

• Translating Functions [Mosley, 08/27/1998]
  Find f(2+h), f(x+h), and f(x+h)-f(x)/h where h cannot = 0 for f(x) = x/(x + 1). Explain how the following graphs are obtained from the graph of y = f(x)...

• Lattice Points and Boundary Lattice Points [Doria, 08/30/1998]
  What is an interior lattice point and a boundary lattice point of a given shape (triangle, circle, rectangle, etc.)?

• Descartes' Method for Tangents [Sara, 09/02/1998]
  Can you help me find the equation of the tangent of y^2 = 2x using Descartes' method...?

• Testing for Horizontal Asymptotes [Thomas, 09/12/1998]
  Is there a rule for testing whether or not an equation has a horizontal asymptote?

• X- and Y-Intercepts [Haun, 09/15/1998]
  I'm having a hard time finding out how to solve an equation and then do the graph. The intercepts confuse me also...

• The General Polynomial Function [Chaithaweep, 09/17/1998]
  How do you relate a polynomial like y=6x-2 to the general polynomial function? How do I graph and find the inverse of y=sqrt(2)?

• Slopes of Perpendicular Lines [Mielke, 09/17/1998]
  Why are the slopes of perpendicular lines negative reciprocals?

• Domain, Range, and Asymptote [Summer, 10/12/1998]
  How do you find the domain, range, and asymptote of a function?

• Deriving the Quadratic Formula [Smith, 10/15/1998]
  How do you derive the quadratic formula from ax^2 + bx + c = 0?

• Non-parallel Glide Reflections [Shubert, 10/21/1998]
  A glide reflection consists of a line reflection and a translation parallel to the reflection. What if the translation is not parallel to the reflection?

• Finding Intervals in Trig Graphs [Sara, 10/25/1998]
  Can you help me with graphing sine and cosine functions? How do you mark off the intervals?

• Definitions of Advanced Concepts [Morrison, 11/13/1998]
  Can you give me definitions for: Pythagorean Triplets, Principle of Duality, Euclid's Elements, Cycloid, Fermat's Last Theorem?

• Graphing an Ellipse [Phil, 11/20/1998]
  How do you graph an ellipse? What is the equation?

• Folium of Descartes and Parametric Equations [Goh, 11/23/1998]
  How do you plot an implicit function, such as the folium of Descartes, with the equation y^3 + x^3 = 3xy?

• An Ellipse Or A Circle? - Parametric Equations [Sands, 12/05/1998]
  Is this parametric equation elliptical or a circle?... And how do I compute the slopes at points 0, pi/4, pi/2, 3pi/2,and 2pi?

• First Principle Hyperbolas [Janis, 01/05/1999]
  How do you solve for the standard equation of a hyperbola given its properties?

• Symmetry Tests [Scardino, 01/12/1999]
  How can you know whether a graph is symmetric to the x-axis, y-axis, or the origin? What does the symmetry mean?

• A Project on Cycloids [Jenny, 01/16/1999]
  Can you explain cycloids? How do you work with the parametric equations? What are their properties? How are they related to time?

• Rotating Parabolas [Wilson, 01/19/1999]
  How do you find a parabola that has a line of symmetry other than a line parallel to the x-axis or y-axis?

• Involute of a Circle [Malone, 01/22/1999]
  What is the formula for the involute of a circle?

• Ellipse Equation [Patrick, 03/11/1999]
  How do I get the equation of an ellipse, given four points and the inclination of the major axis?

• Horizontal and Vertical Asymptotes [Kristin, 03/16/1999]
  For the function y = (5x+1)/(x^2-1), why does the line between its two vertical asymptotes and one horizontal asymptote cross?

• Multiplying or Dividing by a Negative Number [Yap, 04/08/1999]
  When x(x-4) is less than 0...

• Finding the Zeros of a Function [Toni, 05/12/1999]
  How would I find the zeros of P(x) = (x^2-3)(2x-7)^2(x-1)^3, and what is meant by "state the multiplicity of each"?

• Determining Slope [Jaramillo, 05/19/1999]
  How do I find the slope of a line given the coordinates of two points?

• Solving Conic Equations [Whitaker, 05/31/1999]
  Can you show me the steps for solving conic equations and putting them in hyperbola, ellipse, or parabola form?

• Finding the Center of a Circle [John, 06/01/1999]
  How do you find the centre of a circle if you are given 2 points on the circle and the radius?

• Finding the Center of a Circle [Eddie, 06/06/1999]
  How can I find the center and radius of a circle that is in the form: Ax^2 + Cy^2 + Dx + Ey + F = 0?

• Intercept of Two Lines [Burger, 06/07/1999]
  How can you calculate the exact location of the intercept point of two lines without graphing?

• Polynomial Function and Exponential Growth [Roland, 06/08/1999]
  How can I find a polynomial function with integer coefficients that has 3, 2, -4 and -1 as zeroes? What is the population of a colony of bacteria 20 seconds after it is discovered?

• Solving Inequalities [Mandich, 07/13/1999]
  Solve the inequality and express the solution in terms of intervals.

• Equation for a W-Shaped Graph [Clarke, 08/01/1999]
  What sort of equation has a graph that is shaped like a 'W'?

• Intersecting Parabolas [Sergio, 09/15/1999]
  When do the four points of intersection of two parabolas all lie on a circle?

• Complex Numbers in Quadratic Equations [Oya, 11/09/1999]
  How are imaginary numbers used in solving quadratic equations? How can solutions of this type be represented graphically?

• Proof of Perpendicularity [Michael, 10/23/1999]
  How can you prove that two lines (neither vertical) are perpendicular if and only if the product of the gradients is equal to -1?

• Using Cardan's Formula to find Real Roots [Salman, 04/13/2000]
  How can I show that, although the cubic equation x^3 - 6x = 4 has three real solutions, Cardan's formula can find them by subtracting appropriate cube roots of complex numbers?

• Determining Whether a Function is Continuous [Keenan, 06/10/2000]
  How can you tell whether or not a function is continuous?

• Graphing Sine and Cosine [Bernadette, 07/07/2000]
  How do you graph equations that use the sine or cosine functions?

• Definition of a Cone [Romanowski, 07/13/2000]
  I don't see how a right circular cone cut parallel to the axis of symmetry reveals a hyperbola. Shouldn't it be a parabola?

• Finding the Equation of a Curve [Kobayashi-Solomon, 10/02/2000]
  I'm looking for an equation for a curve that describes the way people store information about pending events over time. I would also like to know how to find the equation of any curve.

• The Roses of Grandi [Getz, 11/13/2000]
  The Roses of Grandi are given by polar equations r = a*sin(n*theta) and r = a*cos(n*theta) where n is an integer. How can I show that they are algebraic?

• Graphing Quadratic Polynomials [Gregory, 02/07/2001]
  Can you give me a simple explanation of how to graph quadratic polynomials like y = x^2 - 8x + 15?

• Limit of Cos(Cos( ... Cos(x) ... ))) [Dellinger, 02/24/2001]
  Find the limit of a repeating trigonometric expression cos(cos( ... cos(x) ... )) as the number of cosines goes to infinity.

• X Line in a 3D Graph [Jane, 03/10/2001]
  Which is the x line - vertical or horizontal?

• X = TanX [Andrew, 03/21/2001]
  Show that x = tanx has an infinite number of solutions.

• Point on a Line [Chris, 03/23/2001]
  Can you please tell me a formula to find if a point exists on a line? Both are in x,y form.

• Big O Notation and Polynomials [Paul, 04/12/2001]
  Given the function f(x) = (x^3 - (4x^2) + 12)/(x^2 + 2), how can I find a polynomial function g(x) such that f(x) = O(g(x)) and g(x) = O(f(x))?

• Finding Focus and Directrix [Brent, 04/12/2001]
  How can you find the focus and directrix when given a formula for a parabola?

• Finding the Equation of a Parabola [Rakesh, 04/28/2001]
  How can I find the equation of a parabola whose zeros are at 0 and 6, and whose minimum value is -9?

• Parabola with Horizontal or Vertical Axis [Jamie, 05/03/2001]
  How can I find the focus and directrix of a parabola whose axis is either horizontal or vertical, like 2x^2 = -y?

• Moving a Circle on a Polar Graph [Mike, 05/04/2001]
  How do you move a circle so the center is not (0,0), but to where the center can be (r,[theta])?

• Finding Point of Intersection [Ernst, 05/08/2001]
  Is there a formula to tell if two lines, given by point coordinates, cross and at what coordinates they cross?

• Creating a Smooth Acceleration in Animation [William, 05/09/2001]
  I am trying to figure out a way to set the value of X to achieve a specific difference between the last two sets in this problem...

• Line Dividing a Plane [Jessica, 05/11/2001]
  Given a square (graphed on the Cartesian coordinate system) and a point in the square, draw a line through the point that will divide the square into two regions: one the smallest area possible, the other the largest possible.

• Slope-Intercept Formula [Vittorio, 06/05/2001]
  How come y = mx + b has to be that way?

• Point inside a Triangle [Bob, 07/15/2001]
  Given four points, three of them the corners of a triangle, is there a formula to determine whether or not the fourth is inside the triangle?

• Shape of the Sine Curve vs. Circle [Aaron, 07/18/2001]
  When the equation y = 5sinx is graphed, the curve looks almost linear except near the points where y = 5. Since the sine curve originates from the circle, why isn't it completely curvy like a circle?

• Point Inside or Outside Triangle? [Natalie, 08/02/2001]
  I have coordinates of three vertices of the triangle and coordinates of the point.

• Finding Three Lines that Form a Triangle [Joe, 08/30/2001]
  Find an equation for each of the lines that goes through the point (3,2) forming a triangle of area 12 with the coordinate axes.

• Points Equidistant from Point and Line [Arun, 08/30/2001]
  I have to plot as many points equidistant from a point and a line as possible, and join them to get the locus.

• Recognizing Functions [Miles, 09/30/2001]
  How do I know when there is a function on a graph?

• Graph Theory [Kate, 09/29/2001]
  Why is a graph with five vertices, each having a degree of 3, impossible?

• Graph with f(x) [Angela, 10/17/2001]
  Sketch the equations: y = f(x)+ 2; y = f(x-3); y = 2f(x).

• Points Where a Parametric Equation Crosses Itself [Jessica, 10/12/2001]
  Find all the points where the function of the parametric equation: x= t(9-t^2) and y=(t^2-1)(t^2-9) crosses itself...

• Piecewise Function [Amie, 10/23/2001]
  How do you graph the piecewise function?

• Graphing Reciprocal Functions [Willa, 11/01/2001]
  I know what a reciprocal is, but I don't know how to graph it.

• T-Charts and Graphs [Anjo, 11/11/2001]
  Make a table of values for the line y = x/4+4 using x-values of 1,2,3,4, and 5. Which graph shows the line that passes through the ordered pairs of the table?

• Standard Form in Linear Equations [Nikki, 11/21/2001]
  Where is standard form used?

• Equation of a Parabola [Richard, 12/20/2001]
  Given several points that appear to be a parabola, how do you approximate the equation that would give a similar graph?

• Graphing Linear Equations [Cindi, 12/26/2001]
  Give the intercepts of 7x - 2y = 2.

• Absolute Value Equation with Diagonal Axis of Symmetry [Cob, 01/10/2002]
  What's an example of an absolute value equation where the axis of symmetry is a diagonal line, say y = x?

• Variation Per Unit of Time [John, 02/22/2002]
  Why does the slope of a line correspond to the space that the particle runs per unit of time?

• Equations that Meet on a Graph [Karyn, 03/09/2002]
  Graph d = 30t and d = 28t+12 (d is distance and t is time).

• History of the y-intercept [Chris, 03/18/2002]
  Why does the variable 'b' represent the y-intercept?

• Equation in Slope Intercept or Point Slope Form [Andrea, 03/16/2002]
  Find an equation of the line with slope -4/3 and y-intercept 3. Leave the equation in slope intercept form....

• What We're Doing When We Do Algebra [Mike, 03/25/2002]
  How do you graph x + y = 5 on a graph sheet?

• Oblique Asymptotes [Jo, 04/03/2002]
  I'm stuck on how to calculate oblique limits, for example, x^2/(x-3).