Factored Quadratic Form
CraigsMaths
Mathematics Teaching for Learning
Engineering Maths B, Quadratic Equations
August 5th, 2008 by Craig Rose
Permalink: http://www.craigsmaths.com/ea003-engineering-mathematics-b/factored-quadratic-form/
If a quadratic can be factored it may be expressed in the following form:
This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.
Vertex
To find 
substitute the value of 
into the original equation.
Maxima or minima?
The sign of 
will tell us this.
If negative then the vertex is a maxima. (The “opening” of the parabola points down).
Conversely, if positive then the vertex is a minima. (The “opening” of the parabola points up).
Axis of symmetry
The axis of symmetry will be the line .
intercepts
To find the values for where the parabola touchs or crosses the X-axis we need to put 
.
We can read the intercepts directly from this as the equation is satisfied when 
and 
.
If 
there is only one solution.
If 
there are two real solutions.
intercept
To find the values for where the parabola touchs or crosses the Y-axis we need to put 
.
