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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. Polar Coordinates From Cartesian Coordinates [07/27/1998] How do you find the polar coordinates from the Cartesian coordinate (3, - 3 sqrt(3))? Polar Equation of a Circle [4/12/1997] Given the polar equations r = a*sin (theta) and r = a*cos (theta), what influence does a have on the graph? Polar to Rectangular Conversions [4/19/1996] How do I convert "8 cis 30" into rectangular coordinates? Polynomial Function and Exponential Growth [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? Practical Uses for Computing Parabolas [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? Pre-calculus Function Question [2/8/1996] Does the function f(x)=3De^(1/x) have a local minimum? Proof of Perpendicularity [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? Quadrant [03/25/2001] What is a quadrant? Quadratic Formulas, Equations, Parabolas, Graphing [6/16/1996] Given 6x^2 + x - 1 = 0, how do I find the roots, the vertex, some coordinates, and from these graph it? Quadratic Inequalities [03/18/2003] When I solve (x^2 + 1)/4 greater than or equal to (x + 2)/2 , of my final two answers, only one works. Quintic Equations [1/27/1996] What does Quintic mean? Recognizing Functions [09/30/2001] How do I know when there is a function on a graph? Rectangular Hyperbola [06/11/2002] The graph of a rectangular hyperbola looks nothing like a rectangle. Where does the name come from? Root Multiplicity and Polynomial Functions [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? The Roses of Grandi [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? Rotating Parabolas [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? Shape of the Sine Curve vs. Circle [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? Shifting Graphs [08/26/2002] Why is the graph of y=f(x-c) just the graph of y=f(x) shifted c units to the right? Similar Graphs [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? Sketch a Graph [6/1/1996] z=(3-2i)^1/2, then find z^. Sketching a Function [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) ... Sketching a Polynomial [04/04/2002] Why should a curve change its position or sign at roots? Can't a curve have a positive value for all roots? Sketching Curves [6/24/1996] How do I sketch the curve y = log natural of x/ (1-x)? Slope-Intercept Formula [06/05/2001] Why does y = mx + b have to be that way? Slope of Lines [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? Slopes of Perpendicular Lines [09/17/1998] Why are the slopes of perpendicular lines negative reciprocals? Solve for Radius [09/09/1997] Given a circle through three points, what is the equation for the intersection of the perpendicular bisectors? Solving a Fractional Equation [3/10/1996] Can you help me with this? (M+N)/(N-M) + (M^2+N^2)/(N^2-M^2) - (2M)/(M-N) = ? Solving Conic Equations [05/31/1999] Can you show me the steps for solving conic equations and putting them in hyperbola, ellipse, or parabola form? Solving Inequalities [07/13/1999] Solve the inequality and express the solution in terms of intervals. Standard Form in Linear Equations [11/21/2001] Where is standard form used? The Sum of a Number and Its Reciprocal [11/04/2003] I need a formal proof showing that the sum of a positive number and its reciprocal is at least 2. I can prove it algebraically, but I need a visual justification. Symmetry Tests [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? Tangents to a Curve That Pass through a Fixed Point [08/08/2008] How many tangent lines to the curve y = x/(x+1) pass through the point (1,2)? At which points do those tangent lines touch the curve? T-Charts and Graphs [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? Testing for Horizontal Asymptotes [09/12/1998] Is there a rule for testing whether or not an equation has a horizontal asymptote? Three Points, Two Unknown x-coordinates, All in a Row? [03/04/2013] Given three points, two with unknown abscissas, a student has doubts about their collinearity. After offering some leading hints, Doctor Mike invokes the point-slope form to rigorously confirm the student's suspicions. Translating Functions [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)... Translation [9/11/1996] What does translation mean? TV Transmitters [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. Page: []

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