1. 4.2 Quadratic Equations
Objectives: Solve quadratic equations. Use the discriminant to describe the roots of quadratic equations.

2. Completing the Square:
Quadratic Equations:
A polynomial with degree of two.
ax² + bx + c = 0
Completing the Square:
A process used to create a perfect square trinomial.
x² + 8x + 16
-take half of 8 and square it to get 16
Ex. 1)
Solve x² + 8x + 15 = 0 by completing the square.
*To complete the square, the leading coefficient must be 1. If it isn’t, divide everything by the leading coefficient first.

3. The Quadratic Formula:
Ex. 2)
Solve 4a² + 6a – 3 = 0 by completing the square.
The Quadratic Formula:
If ax² + bx + c = 0, then:
Ex. 3)
A late-night talk show host organized a filming stunt from a 200-foot-tall building. She launched a cantaloupe from the tower’s roof at an upward velocity of 70 ft/s. A film crew recorded the fruit’s messy fall into the roped-off area below. The height of the cantaloupe is given by h(t) = 70t – 16t² where t is the number of seconds since the fruit is launched. How long will it take the cantaloupe to hit the ground?

4. Discriminant:
b² - 4ac → shows the nature of the roots.
b² - 4ac > 0 → 2 real roots
b² - 4ac = 0 → exactly one real root
b² - 4ac < 0 → no real roots
(2 imaginary roots)
Ex. 4)
Find the discriminant of x² + 2x – 2 = 0 and describe the nature of the roots of the equation. Then solve the equation by using the Quadratic Formula.
Conjugates:
a + bi and a - bi
Ex. 5)
Solve 2x² + 3x + 5 = 0