Quadratic Relationships
Unit 2 - Factored Form
Learning Goals
By the end of this unit you should be able to:
- Expand a binomial multiplied by a binomial
- Common factor a polynomial
- Factor complex trinomials and find 2 x-intercepts and vertex
- Factor perfect square trinomials and differences of squares
Summary
An equation in Factored Form looks like this: y = a(x - r) (x - s)
The Variables:
- The value of a gives you the shape and direction of opening
- The value of r and s give you the x-intercepts
Axis of symmetry, AOS: x = (r + s) / 2 -- Sub this x value into the original equation to find the optimal value
To find the y-intercept, set x = 0 and solve for y
Types of Factoring:
- Greatest Common Factor
- Simple Trinomial factoring (a = 1)
- Complex Trinomial factoring
- Special case - Difference of squares
- Special case – Perfect square
Example of a Word Problem
The path of a toy rocket is defined by the relation y = -3x² + 11x + 4, where x is the horizontal distance, in metres, travelled and y is the height, in metres, above the ground.
- Determine the zeros of the relation.
- How far has the rocket travelled horizontally when it lands on the ground?
- What is the maximum height of the rocket above the ground, to the nearest hundredth of a metre?
Solutions:
How to Factor any Quadratic Equation
Factoring Special Products