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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:
Direct and indirect variation.
Slope, slope-intercept, standard form.
- Pre-calculus Function Question [2/8/1996]
Does the function f(x)=3De^(1/x) have a local minimum?
- Proof of Perpendicularity [10/23/1999]
How can you prove that two lines (neither vertical) are perpendicular if
and only if the product of the gradients is equal to -1?
- Quadrant [03/25/2001]
What is a quadrant?
- Quadratic Formulas, Equations, Parabolas, Graphing [6/16/1996]
Given 6x^2 + x - 1 = 0, how do I find the roots, the vertex, some
coordinates, and from these graph it?
- Quadratic Inequalities [03/18/2003]
When I solve (x^2 + 1)/4 greater than or equal to (x + 2)/2 , of my
final two answers, only one works.
- Quintic Equations [1/27/1996]
What does Quintic mean?
- Recognizing Functions [09/30/2001]
How do I know when there is a function on a graph?
- Rectangular Hyperbola [06/11/2002]
The graph of a rectangular hyperbola looks nothing like a rectangle.
Where does the name come from?
- Root Multiplicity and Polynomial Functions [11/16/1997]
What effect does multiplicity [e.g. (x+1)(x-2)^2 where -1 has a
multiplicity of 1 and 2 of 2] have on a polynomial function?
- The Roses of Grandi [11/13/2000]
The Roses of Grandi are given by polar equations r = a*sin(n*theta) and r
= a*cos(n*theta) where n is an integer. How can I show that they are
- Rotating Parabolas [01/19/1999]
How do you find a parabola that has a line of symmetry other than a line
parallel to the x-axis or y-axis?
- Shape of the Sine Curve vs. Circle [07/18/2001]
When the equation y = 5sinx is graphed, the curve looks almost linear
except near the points where y = 5. Since the sine curve originates from
the circle, why isn't it completely curvy like a circle?
- Shifting Graphs [08/26/2002]
Why is the graph of y=f(x-c) just the graph of y=f(x) shifted c units
to the right?
- Similar Graphs [12/11/1995]
How would you describe how the two graphs of y = one over the square root
of x squared and y = one over the square root of x squared minus 4 are
similar and dissimilar?
- Sketch a Graph [6/1/1996]
z=(3-2i)^1/2, then find z^.
- Sketching a Function [07/06/1998]
Can you help me piece a function together so that the following hold? It
is increasing and concave up on (-infinity, 1) ...
- Sketching a Polynomial [04/04/2002]
Why should a curve change its position or sign at roots? Can't a curve
have a positive value for all roots?
- Sketching Curves [6/24/1996]
How do I sketch the curve y = log natural of x/ (1-x)?
- Slope-Intercept Formula [06/05/2001]
Why does y = mx + b have to be that way?
- Slope of Lines [8/6/1996]
What is the slope of the line y = -px + 5 if the line goes through (0, -
3)? Why does the y-axis have an infinite slope, and the x-axis have a
slope of 0?
- Slopes of Perpendicular Lines [09/17/1998]
Why are the slopes of perpendicular lines negative reciprocals?
- Solve for Radius [09/09/1997]
Given a circle through three points, what is the equation for the
intersection of the perpendicular bisectors?
- Solving a Fractional Equation [3/10/1996]
Can you help me with this? (M+N)/(N-M) + (M^2+N^2)/(N^2-M^2) - (2M)/(M-N)
- Solving Conic Equations [05/31/1999]
Can you show me the steps for solving conic equations and putting them in
hyperbola, ellipse, or parabola form?
- Solving Inequalities [07/13/1999]
Solve the inequality and express the solution in terms of intervals.
- Standard Form in Linear Equations [11/21/2001]
Where is standard form used?
- The Sum of a Number and Its Reciprocal [11/04/2003]
I need a formal proof showing that the sum of a positive number and its
reciprocal is at least 2. I can prove it algebraically, but I need a
- Symmetry Tests [01/12/1999]
How can you know whether a graph is symmetric to the x-axis, y-axis, or
the origin? What does the symmetry mean?
- Tangents to a Curve That Pass through a Fixed Point [08/08/2008]
How many tangent lines to the curve y = x/(x+1) pass through the point
(1,2)? At which points do those tangent lines touch the curve?
- T-Charts and Graphs [11/11/2001]
Make a table of values for the line y = x/4+4 using x-values of 1,2,3,4,
and 5. Which graph shows the line that passes through the ordered pairs
of the table?
- Testing for Horizontal Asymptotes [09/12/1998]
Is there a rule for testing whether or not an equation has a horizontal
- Translating Functions [08/27/1998]
Find f(2+h), f(x+h), and f(x+h)-f(x)/h where h cannot = 0 for f(x) = x/(x
+ 1). Explain how the following graphs are obtained from the graph of y =
- Translation [9/11/1996]
What does translation mean?
- TV Transmitters [07/22/1997]
If two TV transmitters are within 150 kilometers of each other, they must
be assigned different channels. Construct a graph that shows the given
problem and use it to find the number of channels needed.
- Types of Linear Systems [10/13/1997]
What is meant when a type of linear system is said to be a consistent or
an inconsistent system?
- Understanding Parametric Equations [04/02/1998]
Can you explain the basic principles of parametric equations?
- Units for Inverse Quantity [9/10/1996]
I have a graph of time vs. 1/distance. What units do I use for 1/
distance - cm^-1?
- Uses for Parametric Equations [04/23/1998]
What is a parametric equation used for? Can you give me an example?
- Using Cardan's Formula to find Real Roots [04/13/2000]
How can I show that, although the cubic equation x^3 - 6x = 4 has three
real solutions, Cardan's formula can find them by subtracting appropriate
cube roots of complex numbers?
- Using Descartes' Method of Tangents [10/2/1995]
Given a point P(3,9) on a parabola y=x^2, how do I find the slope of the
tangent to the parabola at point P using Descartes' method of tangents?