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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Graphing Peculiarity [07/24/2002]

When I use a calculator to graph one form of an equation it works fine; but when I use a different form, it doesn't work. What's going on?

Graphing Polar Equations [06/02/2002]

I need to graph the polar equation (r-3/5)^2 = cos(7 theta), and I don't know how to do it.

Graphing Quadratic Polynomials [02/07/2001]

Can you give me a simple explanation of how to graph quadratic polynomials like y = x^2 - 8x + 15?

Graphing Rational Functions and Vertical Asymptotes [03/28/2008]

When working with rational functions such as y = (x-5)/(x-3), how do you know if the graph curves up or down at the vertical asymptote?

Graphing Reciprocal Functions [11/01/2001]

I know what a reciprocal is, but I don't know how to graph it.

Graphing Sin and Cosine Functions [5/24/1996]

I really need some help in finding the graphs of the following functions...

Graphing Sine and Cosine [07/07/2000]

How do you graph equations that use the sine or cosine functions?

Graphing Slanted Lines [07/22/1997]

When graphing slanted lines what does it mean when the instructions say add, subtract, or divide both sides by a particular number?

Graphing Systems of Equations [06/01/1998]

How do you solve this system of equations by graphing: 3x + 2y = 5 and - 3x - 2y = 10?

Graphing the Absolute Value/Square Root of a Function [07/26/2002]

Can you illustrate and discuss how taking the absolute value or the square root of a function affects the graph of the function?

Graphing Trig Functions [05/03/1997]

How do you graph y = 3sin4x-3?

Graphing Trigonometry Equations [5/15/1996]

How do I graph this one: Sin A - Cos A ?

Graphing without the Y [01/28/2004]

I'm trying to graph the inequality x > -5, but without a y, how can I graph it?

Graph of Circle as a Function [05/30/1998]

The graph of a circle is not a function because it fails the vertical line test. How could you make it a function?

The Graph of f [7/3/1996]

Where are its local and absolute maxima and minima? What are the x- intercepts of the graph of f?...

Graph of y = arcsin x [03/31/2003]

Understanding the graph of arcsin(x).

Graphs of Step Functions [11/29/2003]

Why do some graphs move in steps rather than smooth lines? What causes that?

Graph the Ellipse... [01/01/1998]

[((x-1)^2)/2^2] + [((y-2)^2)/2^2] = 1. Graph the ellipse and find the major and minor axes, the foci, the eccentricity, and the center.

Graph Theory [09/29/2001]

Why is a graph with five vertices, each having a degree of 3, impossible?

Graph with f(x) [10/17/2001]

Sketch the equations: y = f(x)+ 2; y = f(x-3); y = 2f(x).

Greatest Integer Equation [08/06/2003]

I am trying to correctly interpret [[x]]^2 + [[y]]^2 = 1, where f(x)= [[x]], is the Greatest Integer function.

Height and Weight [10/30/1996]

How do you find a formula that predicts a person's weight when all you know is his/her height?

History of the y-intercept [03/18/2002]

Why does the variable 'b' represent the y-intercept?

HP-38G Graphic Calculator [08/29/1998]

I'm having trouble graphing on my HP-38G calculator. Can you help?

Intercept Equation [10/07/1998]

I found a plane using the intercepts (4,0,0), (0,-5,0), and (0,0,3). Now I want an equation for those points using Ax + By + Cz = D.

Intercept of Two Lines [06/07/1999]

How can you calculate the exact location of the intercept point of two lines without graphing?

Intercepts of Quadratic Functions [12/10/2003]

Why do some quadratic functions have two x-intercepts and one y-intercept?

Intersecting Parabolas [09/15/1999]

When do the four points of intersection of two parabolas all lie on a circle?

Intersection of a Parabola and a Line [10/19/2003]

What equation would you use to determine the x-coordinates of the points of intersection of a quadractic function ax^2 + bx + c with the line y = x?

Introduction to Quadrants in the Coordinate Plane [02/05/2004]

What is a quadrant? How do you find it? I had to identify 9 ordered pairs on a graph. Now I need to also name the quadrant each one is in.

Inverse Function [9/15/1996]

Given f(x) = 1 - 2/x what is f-1(x) ?

Inverse Function for Natural Numbers [6/10/1996]

I've got a question about the function n = 0.5((a+b)^2+3a+b), which is a one-to-one bijection from pairs (a,b) of natural numbers to single natural numbers n.

Is It Really Possible to Draw a Graph? [02/01/2007]

Since graphs are collections of points, and points have no dimensions (depth, length, height), we can't really draw a graph. All we can do is make a "representative graph". Is that right?

Is y = abs (x) Continuous? [8/29/1996]

Is y equals the absolute value of x a continuous function?

Lagrange Polynomial Interpolation [08/08/1997]

Please give me the definition and a brief example of how it works.

Lattice Points and Boundary Lattice Points [08/30/1998]

What is an interior lattice point and a boundary lattice point of a given shape (triangle, circle, rectangle, etc.)?

Linear Equations and Standard Form [04/04/2002]

What do the variables mean in the standard form of a linear equation (ax+by=c)?

Line Crossing Horizontal and Vertical Asymptotes [03/16/1999]

For the function y = (5x+1)/(x^2-1), why does the line between its two vertical asymptotes and one horizontal asymptote cross?

Line Dividing a Plane [05/11/2001]

Given a square (graphed on the Cartesian coordinate system) and a point in the square, draw a line through the point that will divide the square into two regions: one the smallest area possible, the other the largest possible.

Line of Best Fit [8/1/1996]

Are a best-fit line, a line of best fit, and a fitted line synonymous?

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