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 TOPICS This page:   equations, graphs   translations    Search   Dr. Math See also the Internet Library:   graphing equations HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Equations, Graphs, Translations Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Asymptotes.     Direct and indirect variation.     Slope, slope-intercept, standard form. Lattice Points and Boundary Lattice Points [08/30/1998] What is an interior lattice point and a boundary lattice point of a given shape (triangle, circle, rectangle, etc.)? Linear Equations and Standard Form [04/04/2002] What do the variables mean in the standard form of a linear equation (ax+by=c)? Line Crossing Horizontal and Vertical Asymptotes [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? Line Dividing a Plane [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. Line of Best Fit [8/1/1996] Are a best-fit line, a line of best fit, and a fitted line synonymous? Lines and t-tables [11/09/1996] How do you use t-tables to graph lines? Lines Partitioning a Plane [03/09/1998] Into how many disjoint regions do n coplanar lines partition the plane? Lines Tangent to a Hyperbola [07/14/1998] If y = 2x + k is a line tangent to the graph x^2 + y^2 = 1, what is k? Locus of the Midpoint of a Chord [03/13/1998] Show that the locus of the midpoint of the chord is a hyperbola. Manipulating Roots [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. Mapping 3D Line Segments [10/06/1997] How do I map 3D line segments onto a 2D perspective as seen from an arbitrary point in space? Minimum Distance [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? More Questions on Finding the Equation of a Circle [10/1/1995] Find the equation of the circle containing the points (-1, -2) and (6,-1) and touching the x-axis. Moving a Circle on a Polar Graph [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])? Multiplying or Dividing by a Negative Number [04/08/1999] When x(x-4) is less than 0... Naming and Graphing Functions [06/16/1997] Can you tell me about the different families of functions? Non-parallel Glide Reflections [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? Oblique Asymptote [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 )... Oblique Asymptotes [04/03/2002] I'm stuck on how to calculate oblique limits, for example, x^2/(x-3). Order of Quadrant Numbers [10/21/2002] Why are quadrants numbered that way? Parabola [12/23/1997] Find the vertex, axis of symmetry, directrix, focus, distance from the vertex to the focus, and the latus rectum. Parabola Equation [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)... Parabola Equations [05/12/1997] Deriving the standard equation for a parabola from its focus and directrix; manipulating this equation to change the graph's appearance. Parabola Focal Point [7/3/1996] What are the rules for the focal point of a parabola? Parabola Problems [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? Parabolas Through Pairs of Points [07/13/2002] Can infinitely many parabolas pass through any two points in a plane? Parabola with Horizontal or Vertical Axis [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? Parabolic Equation of an Arch [05/25/1998] Finding the equation of the parabola in the McDonald's golden arches. Parametric Equations [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... Perpendicular Distance [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). Piecewise Function [10/23/2001] How do you graph the piecewise function? Piecewise Functions on TI Graphing Calculators [02/08/2005] I was wondering if you could tell me how to graph a piecewise function on a TI-83 plus graphing calculator? Piecewise Notation and Absolute Value [9/9/1996] How do I use piecewise notation to write x in terms of y for "y=2x+ abs(2-x)"? Point Contained by a Circle [8/8/1995] How can I tell if an arbitrary point on a plane is contained by a circle? Point inside a Triangle [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? Point Inside or Outside Triangle? [08/02/2001] I have coordinates of three vertices of the triangle and coordinates of the point. Point on a Line [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. Points Equidistant from Point and Line [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. Points Where a Parametric Equation Crosses Itself [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... Polar Coordinates and Logarithmic Spirals [04/25/2004] The polar coordinate graph of a logarithmic spiral suggests that for a given angle, there is more than one possible r-value, since the graph continues to spiral around itself. How is it possible for an angle to be associated with more than one r? Page: []

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