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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.

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.

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

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