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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. A Cubic Curve, Its Double Root, and Its Integer Solutions [02/27/2011] A student seeks integer solutions to (x^2 + y)(x + y^2) = (x - y)^3. To oblige, Doctor Vogler parameterizes the equation of this twisted curve. Cubic Polynomial [6/27/1996] Show that the graph of every cubic polynomial has a point of symmetry. Curve Fitting [03/08/1997] I need help writing an algorithm that fits a curve to a given set of data points. Curvy ... and Topsy-Turvy? [11/22/2014] Inspecting the zeros of a polynomial, a teen wonders why its plot resembles the graphs of its constituent terms, but with the signs reversed. Doctor Peterson explains the contrary curves with numerical approximation; Doctor Greenie, with a logical extension. Data that Decay, and a Curve to Fit Them [07/09/2012] What curve models a frequency table of data that tail off to zero? Doctor Douglas outlines how to curve-fit data before tracking down their source. Decimal to Polar Coordinates [11/23/1997] I need to know how to convert from rectangular coordinates back to polar. Definition of a Cone [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? Definition of a Parabola [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... Definitions of Advanced Concepts [11/13/1998] Can you give me definitions for: Pythagorean Triplets, Principle of Duality, Euclid's Elements, Cycloid, Fermat's Last Theorem? Degenerate Conics [03/04/1998] Identifying the degenerate cases for the graphs of equations in conic form. Deriving the Hyperbola Formula [04/27/1998] When speaking of hyperbolas, why does C^2 = A^2 + B^2? Deriving the Quadratic Formula [10/15/1998] How do you derive the quadratic formula from ax^2 + bx + c = 0? Descartes' Method for Tangents [09/02/1998] Can you help me find the equation of the tangent of y^2 = 2x using Descartes' method...? Describing the Graph of an Equation [1/27/1996] Which of the following is true of the graph of the equation: y = 2x^2 - 5x + 3 ?... Determining Linear Relations [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? Determining Slope [05/19/1999] How do I find the slope of a line given the coordinates of two points? Determining Tangent to an Ellipse, Minimizing Area [02/20/1998] Find the equation of the tangent to the ellipse that forms, with the coordinate axes, the triangle of smallest possible area. Determining Whether a Function is Continuous [06/10/2000] How can you tell whether or not a function is continuous? Difference Quotient Function [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. Dilations of the Graph of y = f(x) [08/22/2004] If y = 2f(x) stretches y = f(x) vertically by a factor of 2, why does y = f(2x) shrink it horizontally by a factor of 2? The notation seems inconsistent. Direct and Indirect Variation [07/09/1998] Can you explain the difference between direct and indirect variation? How would you interpret them in a word problem? Direct/Indirect Variation [6/12/1996] Please explain direct and indirect variation. Domain of a Function [9/13/1996] What is the domain of f(x)= x/sqrt(x^2-4)? Domain, Range, and Asymptote [10/12/1998] How do you find the domain, range, and asymptote of a function? Domain, Range, and Translating Functions [06/29/2004] Given the graph of y = f(x), domain [-4,3], range [-2,3], sketch other functions, such as y = |f(x)| and y = f(x - 2), and find the domain and range of each. Domain/Range of a Function [01/22/1997] How do you find the domain and range of the function f(x) = 2x^2-3x+1? (Both with and without calculus.) Drawing a Line, Given the Slope and One Point [05/23/2002] How do I draw a line on a graph when I know the slope and the location of only one point on the line? Drawing Spirals on Your Computer [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? Ellipse Equation [03/11/1999] How do I get the equation of an ellipse, given four points and the inclination of the major axis? An Ellipse Or A Circle? - Parametric Equations [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? Equation for an Ellipse [10/27/1995] I found the right formula for a circle but can't find it for an ellipse. Equation for a Vertical Line [8/29/1996] What is equation for a vertical line passing through (7, -10)? Equation for a W-Shaped Graph [08/01/1999] What sort of equation has a graph that is shaped like a 'W'? Equation in Slope Intercept or Point Slope Form [03/16/2002] Find an equation of the line with slope -4/3 and y-intercept 3. Leave the equation in slope intercept form.... The Equation of a Cone [9/13/1995] I would like to know the equation of a cone. Could you help me? Equation of a Line [01/27/1998] How do I find the equation of a line through origin perpendicular to 2x + 3y = 5? Equation of a Line in Point-Slope, Slope-Intercept, General Form [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 a Parabola [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. Equation of a Parabola [12/20/2001] Given several points that appear to be a parabola, how do you approximate the equation that would give a similar graph? Equation of a Rectangle? [11/11/2012] A student wonders if there is an equation for a rectangle in the Cartesian plane, comparable to the one for the equation of a circle. Doctor Peterson confirms the student's suspicions about the difficulties involved. Page: []

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