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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:
Asymptotes.
Direct and indirect variation.
Slope, slopeintercept, standard form.
 Practical Uses for Computing Parabolas [1/30/1996]

Could you give me three practical uses for computing parabolas and tell
me the significance of computing the parabola in regard to its
application?
 Precalculus 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)(x2)^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
algebraic?
 Rotating Parabolas [01/19/1999]

How do you find a parabola that has a line of symmetry other than a line
parallel to the xaxis or yaxis?
 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(xc) 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=(32i)^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/ (1x)?
 SlopeIntercept 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 yaxis have an infinite slope, and the xaxis 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)/(NM) + (M^2+N^2)/(N^2M^2)  (2M)/(MN)
= ?
 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
visual justification.
 Symmetry Tests [01/12/1999]

How can you know whether a graph is symmetric to the xaxis, yaxis, 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?
 TCharts and Graphs [11/11/2001]

Make a table of values for the line y = x/4+4 using xvalues 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
asymptote?
 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 =
f(x)...
 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?
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