## Learning Goals

By the end of this unit you should be able to:

• determine max/min values of a quadratic relation using zeroes and symmetry
• convert a quadratic relation from standard form to vertex form (complete the square)
• solve real-world problems involving max/min

## Summary

An equation in Factored Form looks like this: y = ax² + bx + c

The Variables:

• the value of a gives you the shape and direction of opening
• the value of c is the y-intercept

To get the x-intercepts, solve using the quadratic formula.

The number inside the square root (b² - 4ac) of the quadratic formula is called the Discriminant (D). It helps us tell how many solutions the quadratic equation will have without having to use the whole formula.

When D < 0, there will be no solutions (x-intercepts). When D > 0, there will be 2 solutions. And when D = 0, there will be only 1 solution.

Use the completing the square method to convert standard form into vertex form.

## Example of a Word Problem

The path of a basketball after it is thrown in the air is given by the following equation:

h = -0.25d² + 2d + 1.5, where h is the height and d is the horizontal distance in metres.

1. What is the initial height of the basketball?
2. What is the maximum height reached by the basketball and at what horizontal distance does this occur at?

Solutions: