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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, slopeintercept, 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 TopsyTurvy? [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 curvefit 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^24)?
 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^23x+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 WShaped 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 yintercept 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 PointSlope, SlopeIntercept, 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 2x5y+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.
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