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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Lines and t-tables [11/09/1996]

How do you use t-tables to graph lines?

Lines Partitioning a Plane [03/09/1998]

Into how many disjoint regions do n coplanar lines partition the plane?

Lines Tangent to a Hyperbola [07/14/1998]

If y = 2x + k is a line tangent to the graph x^2 + y^2 = 1, what is k?

Locus of the Midpoint of a Chord [03/13/1998]

Show that the locus of the midpoint of the chord is a hyperbola.

Manipulating Roots [08/08/1998]

If a and b are the roots of the equation 3x^2 - 5x + 1 = 0, find the equation whose roots are a/b and b/a.

Mapping 3D Line Segments [10/06/1997]

How do I map 3D line segments onto a 2D perspective as seen from an arbitrary point in space?

Minimum Distance [02/07/1998]

What is the minimum possible distance between a point on the graph of x^2+y^2 = 1 and a point on the graph of xy = 1?

More Questions on Finding the Equation of a Circle [10/1/1995]

Find the equation of the circle containing the points (-1, -2) and (6,-1) and touching the x-axis.

Moving a Circle on a Polar Graph [05/04/2001]

How do you move a circle so the center is not (0,0), but to where the center can be (r,[theta])?

Multiplying or Dividing by a Negative Number [04/08/1999]

When x(x-4) is less than 0...

Naming and Graphing Functions [06/16/1997]

Can you tell me about the different families of functions?

Non-parallel Glide Reflections [10/21/1998]

A glide reflection consists of a line reflection and a translation parallel to the reflection. What if the translation is not parallel to the reflection?

Oblique Asymptote [4/13/1996]

I have a question about the oblique asymptote of the function: F( X ) = ( X^3 - 3X^2 + 2X - 8 ) / ( X^2 + 4X + 4 )...

Oblique Asymptotes [04/03/2002]

I'm stuck on how to calculate oblique limits, for example, x^2/(x-3).

Order of Quadrant Numbers [10/21/2002]

Why are quadrants numbered that way?

Parabola [12/23/1997]

Find the vertex, axis of symmetry, directrix, focus, distance from the vertex to the focus, and the latus rectum.

Parabola Equation [5/15/1995]

I'm trying to learn equations of parabolas. The example given is: find the equation of the parabola with vertex (0,0) and focus (0,-3)...

Parabola Equations [05/12/1997]

Deriving the standard equation for a parabola from its focus and directrix; manipulating this equation to change the graph's appearance.

Parabola Focal Point [7/3/1996]

What are the rules for the focal point of a parabola?

Parabola Problems [2/23/1997]

A culvert is shaped like a parabola, 18 centimeters across the top and 12 centimeters deep. How wide is the culvert 8 centimeters from the top?

Parabolas Through Pairs of Points [07/13/2002]

Can infinitely many parabolas pass through any two points in a plane?

Parabola with Horizontal or Vertical Axis [05/03/2001]

How can I find the focus and directrix of a parabola whose axis is either horizontal or vertical, like 2x^2 = -y?

Parabolic Equation of an Arch [05/25/1998]

Finding the equation of the parabola in the McDonald's golden arches.

Parametric Equations [07/21/1998]

A curve is given parametrically by the equations: x = (3-2k)^2 and y = (2+k)^2. Find dy/dx, the x-intercept, the cartesian equation...

Perpendicular Distance [04/10/1998]

Prove that the distance from a line ax + by + c = 0 to the point (h,k) is (a*h + b*k + c)/(a^2+b^2)^(1/2).

Piecewise Function [10/23/2001]

How do you graph the piecewise function?

Piecewise Functions on TI Graphing Calculators [02/08/2005]

I was wondering if you could tell me how to graph a piecewise function on a TI-83 plus graphing calculator?

Piecewise Notation and Absolute Value [9/9/1996]

How do I use piecewise notation to write x in terms of y for "y=2x+ abs(2-x)"?

Point Contained by a Circle [8/8/1995]

How can I tell if an arbitrary point on a plane is contained by a circle?

Point inside a Triangle [07/15/2001]

Given four points, three of them the corners of a triangle, is there a formula to determine whether or not the fourth is inside the triangle?

Point Inside or Outside Triangle? [08/02/2001]

I have coordinates of three vertices of the triangle and coordinates of the point.

Point on a Line [03/23/2001]

Can you please tell me a formula to find if a point exists on a line? Both are in x,y form.

Points Equidistant from Point and Line [08/30/2001]

I have to plot as many points equidistant from a point and a line as possible, and join them to get the locus.

Points Where a Parametric Equation Crosses Itself [10/12/2001]

Find all the points where the function of the parametric equation: x= t(9-t^2) and y=(t^2-1)(t^2-9) crosses itself...

Polar Coordinates and Logarithmic Spirals [04/25/2004]

The polar coordinate graph of a logarithmic spiral suggests that for a given angle, there is more than one possible r-value, since the graph continues to spiral around itself. How is it possible for an angle to be associated with more than one r?

Polar Coordinates From Cartesian Coordinates [07/27/1998]

How do you find the polar coordinates from the Cartesian coordinate (3, - 3 sqrt(3))?

Polar Equation of a Circle [4/12/1997]

Given the polar equations r = a*sin (theta) and r = a*cos (theta), what influence does a have on the graph?

Polar to Rectangular Conversions [4/19/1996]

How do I convert "8 cis 30" into rectangular coordinates?

Polynomial Function and Exponential Growth [06/08/1999]

How can I find a polynomial function with integer coefficients that has 3, 2, -4 and -1 as zeroes? What is the population of a colony of bacteria 20 seconds after it is discovered?

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?

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