Ask Dr. Math

High School Archive

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.

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Evaluating Composite Functions [1/31/1996]

If f(x) = 3, and g(x) = x^2 + 1 divided by the square root of (x^2 -1), how do you evaluate the composite function of f composed with g (f circle g)?

Finding a Point Equidistant From Two Other Points [8/18/1996]

Point A is (-5,-3), and point B is (-1,-5); to be equidistant from A and B, what should the value of k be for the point (3,k)?

Finding a Point on a Circle [5/28/1996]

How do I find the y1 value?

Finding Asymptotes [07/06/1998]

In the equation y = (m/x) + c, how do the values of m and c affect the graph? How do you find the asymptotes?

Finding Equations of Parabolas [12/12/1996]

Determine the equation of the parabola whose vertex is at (1,3) and whose directrix is y=x.

Finding Focus and Directrix [04/12/2001]

How can you find the focus and directrix when given a formula for a parabola?

Finding Intervals in Trig Graphs [10/25/1998]

Can you help me with graphing sine and cosine functions? How do you mark off the intervals?

Finding Point of Intersection [05/08/2001]

Is there a formula to tell if two lines, given by point coordinates, cross and at what coordinates they cross?

Finding the Center of a Circle [06/06/1999]

How can I find the center and radius of a circle that is in the form: Ax^2 + Cy^2 + Dx + Ey + F = 0?

Finding the Equation of a Curve [10/02/2000]

I'm looking for an equation for a curve that describes the way people store information about pending events over time. I would also like to know how to find the equation of any curve.

Finding the Equation of a Line [01/08/1997]

Given either a point and a slope or two points, how do you find the equation of a line in both point-slope and standard form?

Finding the Equation of a Parabola [04/28/2001]

How can I find the equation of a parabola whose zeros are at 0 and 6, and whose minimum value is -9?

Finding the Equations of Two Circles [9/30/1995]

Find the equation of the circles with the center at (4,-7) and touching (externally and internally) the circle with the equation: (X^2)+(Y^2)+4X- 2Y+1=0.

Finding the Table's Diameter [05/05/2001]

A circular table is pushed into the corner of a room so that it touches both walls. On the edge of the table is a scratch 8" from one wall and 9" from the other wall. What is the diameter of the table?

Finding the Zeros of a Function [05/12/1999]

How would I find the zeros of P(x) = (x^2-3)(2x-7)^2(x-1)^3, and what is meant by "state the multiplicity of each"?

Finding Three Lines that Form a Triangle [08/30/2001]

Find an equation for each of the lines that goes through the point (3,2) forming a triangle of area 12 with the coordinate axes.

First Principle Hyperbolas [01/05/1999]

How do you solve for the standard equation of a hyperbola given its properties?

Folium of Descartes and Parametric Equations [11/23/1998]

How do you plot an implicit function, such as the folium of Descartes, with the equation y^3 + x^3 = 3xy?

Formula for a Helix [07/08/1997]

What is the formula that gives the height above the ground of a point on a helix?

The General Polynomial Function [09/17/1998]

How do you relate a polynomial like y=6x-2 to the general polynomial function? How do I graph and find the inverse of y=sqrt(2)?

Generating Fractal Equations [7/1/1996]

Is there any way to generate a fractal equation from a set of numbers?

Given n Points, find a Polynomial Function... [6/27/1996]

Find a polynomial F(x) of degree less than n so that the graph of F passes through all of the points.

Graphing Absolute Values [07/03/2002]

I have a function, f(x), that I can graph, but I don't understand how to graph |f(x)|.

Graphing a Circle [04/14/1998]

I would like to know how to graph the equation of a circle.

Graphing a Function with Asymptotes [07/05/1998]

How do you find the asymptotes of f(x) = (2x + 1)/(x - 3)? How do you use the asymptotes to graph the function?

Graphing a Line Given a Point on It and Its Slope [03/07/2004]

I am completely confused about how to graph lines. The question is asking me to graph the line that goes through the point (0,2) with a slope m = 1/4. I am not sure what slope m = 1/4 means.

Graphing and Understanding Conic Equations [12/11/1995]

How can I sketch and find the vertices of this conic equation?

Graphing an Ellipse [11/20/1998]

How do you graph an ellipse? What is the equation?

Graphing an Equation [11/08/1997]

Please explain how to graph this equation: y = a + b(x) + c(x^2) + ...

Graphing a Parabola [4/3/1995]

How do you graph the quadratic equation, y=3(x+1)^2 -20?

Graphing Complex and Real Numbers [02/26/2003]

Since on the Cartesian plane we can only graph real zeros and real solutions, are we truly graphing the function when we omit the complex and imaginary zeros and solutions?

Graphing Direct Variation [02/27/2003]

How do you graph direct variation? I thought you had to have two coordinates to graph a line.

Graphing Equations [08/15/1997]

I know the coordinates of these equations, but what are the names and how do I graph them?

Graphing f(2x) and f(|x|) [09/03/2003]

Given f(x), how do you graph f(2x) and f(|x|)?

Graphing Inequalities [06/05/2003]

How do you graph y + 4x is less than 20 ?

Graphing Intercepts [11/06/1997]

How would I find the intercept for a problem such as 3x-2y = 12?

Graphing Linear Equations [07/14/1998]

Can you give me a step by step guide to graphing linear equations?

Graphing Linear Equations [12/26/2001]

Give the intercepts of 7x - 2y = 2.

Graphing Multivariable Polynomials [02/20/2005]

I have a few questions about multivariable polynomials. Say we have the polynomial x + y + z, can this be graphed? I also really don't know anything about the z axis or how to graph on it.

Graphing Parabolas [01/16/1997]

How do you know how to graph a parabola from looking at its equation?

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