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.

1 Equation in Degree 2 with 3 Variables [09/23/2017]

Given only one equation, an adult struggles to make headway solving for its three variables. Doctor Ian completes three squares, then introduces Diophantines and the ellipsoid graph of the equation.

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.

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