CraigsMaths

Mathematics Teaching for Learning

Parabolas

August 5th, 2008

A parabola is a curve that is described by a quadratic equation. You may be presented with a quadratic equation in one of several forms and then asked to:

  • Sketch a graph of the equation
  • Find the local maxima or local minima
  • Find the vertex coordinates
  • Find the x-intercept(s) if they exist
  • Find the the y-intercept
  • Find the axis of symmetry

This article will describe the simplest approach for the different forms of the quadratic equation.

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General Quadratic Form

August 5th, 2008

The general quadratic form is:

y=ax^{2}+bx+c

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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Factored Quadratic Form

August 5th, 2008

If a quadratic can be factored it may be expressed in the following form:

y=a(x+h)(x+k)

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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Standard Quadratic Form

August 1st, 2008

This is the “standard” form of the quadratic equation:

y=a(x-h)^{2}+k where a\neq0

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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Cramer’s Rule

July 30th, 2008

Given a system of simultaneous equations in matrix form

Simultaneous equations in matrix form

Where is an invertable n x n square matrix, is a variables column matrix containing and is a constants matrix containing .

Then can be found with Cramer’s rule,

Cramers rule

Cramer's rule

Where is formed by replacing the ith column of with .