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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Changing a Trigonometric Graph [08/06/1998]

How do you graph: -cos 2x / 2?

Converting and Graphing Coordinates [5/28/1996]

How do you convert a decimal to a polar coordinate and graph it?

Curve Fitting [12/13/1996]

How do you convert points on a graph to a line?

Equation of a Line Parallel to an Axis [06/19/2003]

How can I get the equation of a line if the line passes through a point and is parallel to the x- or y-axis?

Equations of a Line given Two Points [8/31/1996]

How do you find the equation of a line going through two points if you only know the two points?

Finding y-intercepts [6/12/1996]

I'm having a problem with finding and graphing y-intercepts of linear equations.

Formula for Point in Rectangle [5/31/1996]

I need a formula that will allow me to determine whether or not a specified point lies within a rectangle.

Geometric Objects and Properties using Algebra [06/29/1998]

Why does y = mx+b, and what does it mean?

Graphing Coordinates [1/15/1997]

How can you tell if you have a straight line just by looking at the numbers?

Graphing Linear Equations [04/11/2003]

How do I find the points on the line so that I can find the slope and the y-intercept?

Graphing y = mx+b [6/28/1996]

I don't understand what y = mx+b means and how to do slope intercept form.

An Introduction to Parabolas [02/04/1999]

What is a parabola? What are some of its properties? What are some examples of parabolas in real life?

Line of Best Fit [07/08/2003]

I am looking for help in how to manually find the slope and intercept of this problem.

Nomographs [06/12/2003]

What are nomographs used for? How does one use them? Are they still in use? and last but not least, How are they constructed?

Non-Algebraic Explanation of a Parabola [05/16/2000]

What does a parabola look like? How is it formed?

No Solution, Infinite Solutions [01/03/2002]

Solve: 8(2x-3) = 4(4x-8); -3(x-3) is greater than or equal to 5-3x.

Rational Inequality [10/09/2001]

Solve this rational inequality and give an answer in interval notation: - 5/(3h+2) greater than or equal to 5/h.

Simplify this equation: (x+y)/(y^2-xy-y+x) + (y+1)/(xy-x-y+1) + (x+1)/(x^ [8/18/1995]

A rare '"live" talk session with Dr. Math about factoring an equation.

Slope Angle [06/17/2003]

What units do we use to refer to slope?

Stem-and-leaf Graph or Stemplot [10/12/1997]

Can you explain a stem leaf graph?

Tables, Graphs, and Equations [09/04/2001]

Make a table of values to determine the coordinates of three points that lie on the graph of y = 3x+5. Use the headings x, 3x = 5,y, and (x,y). Then...

Translating Parabolas and Completing the Square [5/23/1995]

Parabolas translated from the origin, and standard equations. State the coordinates of the vertex, and sketch the graph of y^2+8y+8x-8=0.

When is a Slope 0 or Undefined? [3/29/1997]

How do I know when the slope of an equation is zero or undefined (no slope)?

Working with Two Equations using Graphs [01/16/2002]

You estimate that you can make muffins for $.30 each. Advertising will cost $18.00. You sell the muffins for $.75 each. Write and graph equations to represent income and expenses. Find the break-even point.

2D Graphing Software: Maple [7/15/1996]

Could you recommend any PC software that could help me study hyperbolas and other curves?

3-D Points to a 2-D computer screen [07/25/1997]

I am trying to write a 3-D graphics engine that takes 8 points with their own (X,Y,Z) coordinates to plot a CUBE in 3-D space...

About Hyperbolas [8/7/1996]

Find the graph and the equation of a hyperbola.

Absolute Value Equation with Diagonal Axis of Symmetry [01/10/2002]

What's an example of an absolute value equation where the axis of symmetry is a diagonal line, say y = x?

Analyzing Range of Function with and without Calculus [08/19/2007]

Show that for all real values of x, the graph of (x^2 + x + 1)/(x + 1) does not lie between -3 and 1 on the y-axis.

Arc Midpoint [07/17/2001]

I'm trying to figure out the midpoint of an arc where I know the start and end points of the arc and the radius only.

Asymptote for (x-4)/x^2 [04/10/2002]

For the function (x-4)/x^2 there is a horizontal asymptote at y=0; however, at x=4 y=0 the graph of the function does intersect the line that is supposed to be the asymptote. How can this be if by definition the asymptote is a line that the function gets close to but does not touch?

Bezier Splines [12/03/1996]

What are the equations for Bezier splines? How would I graph them?

Big O: 2 Functions Map from N to N+ [6/25/1996]

If f, g: N -> N+, then either f(x) is O(g(x)) or g(x) is O(f(x)). Why?

Big O Notation and Polynomials [04/12/2001]

Given the function f(x) = (x^3 - (4x^2) + 12)/(x^2 + 2), how can I find a polynomial function g(x) such that f(x) = O(g(x)) and g(x) = O(f(x))?

Changing Equations To Slope-Intercept Form [07/17/1998]

Can you explain how to change equations into slope-intercept form? For example, 12(2x-1) - 5(3y+2) = 8?

Complex Numbers in Quadratic Equations [11/09/1999]

How are imaginary numbers used in solving quadratic equations? How can solutions of this type be represented graphically?

Composite Functions [4/5/1996]

1) fog(x) = 7x + 3; gof(x) = 7x - 3; f(0) = 1; g(0) = .....

Connecting the Dots [02/02/1998]

How do you know whether or not to connect the dots when graphing a real- life function?

Coordinates of a Point [6/12/1996]

ABC is a right-angled triangle labeled counter-clockwise with its point C lying on the line y=3x. A is (2,1) and B is (5,5). Find the two possible coordinates of C.

Creating a Smooth Acceleration in Animation [05/09/2001]

I am trying to figure out a way to set the value of X to achieve a specific difference between the last two sets in this problem...

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