5.8 The Quadratic FormulaObjectives:1. To solve quadratic

equations by using the Quadratic Formula

2. To determine types of solutions by using the discriminant.

Quadratic Formula

𝒙=−𝒃±√𝒃𝟐−𝟒𝒂𝒄𝟐𝒂

How did we come up with this Quadratic Formula???

Example 1: Solve by using the quadratic formula.

a) b)

Example 1: Solve by using the quadratic formula.

c) d) 41

Example 1: Solve by using the quadratic formula.

e)

Trivia…1. What state has the nickname "The Sunshine State?"

Florida

2. The Mall of America is located in which state? Minnesota

3. What number did Michael Jordan wear when he first returned to the Bulls in 1995?

45

Discriminant

Value of the Discriminant

Type & # of Solutions

Examples of Graphs

2 REAL Solutions

1 REAL Solution

No Real Solutions – 2 Imaginary

Solutions

Example 2: Evaluate the discriminant of each quadratic. Tell how many solution each equation has and whether the solutions are real or imaginary.

a) b)

c) d)

You try…

a) b)

c) d)

e) f)

Evaluate the discriminant of each quadratic. Tell how many solution each equation has and whether the solutions are real or imaginary. Then find the solutions.

Homework P 293 7 – 21 odd, 31 – 39 odd