9.4 Solving Quadratic Equations Standard Form: How do we solve this for x?

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Presentation transcript:

9.4 Solving Quadratic Equations Standard Form: How do we solve this for x?

Ex 1) Solve for x: 2x 2 – 32 = 0

Ex 2) Solve for x: – x = 0

Ex 3) Solve for x: x 2 – 72 = 0

Ex 4) Solve for x: 2x 2 + 7x = –3

Steps to solve by Factoring: 1)Rewrite in Standard Form 2)Factor 3)Use the Zero Product Property If ab = 0, then a = 0 or b = 0.

3 Methods: 1)Isolate x 2, and take the Square Root 2) Factor, split, & solve 3)Use the Quadratic Formula

Solve for x: 1) 2) How do we solve this? 9.5 Solving Quadratic Equations

Steps: 1)Rewrite in Standard Form 2)Identify a, b, & c 3)Substitute a, b, & c into Quadratic Formula and Evaluate.

Ex 1: Solve for x.

1st Rewrite in Standard Form 2nd Identify a, b, & c

3rd Substitute a, b, & c into Quadratic Formula and Evaluate.

The Quadratic Formula If, Then,

Warm-Up Solve for x: 3x 2 – 5x – 1 = 0

Ex 2: Solve for x: 2x 2 – 3x + 7 = 0

The Discriminant D > 0 (positive) 2 Real Solutions D = 0 1 Real Solution D < 0 (negative) No Real Solutions

Homework: