Warm – Up # 9 Factor the following: 3x2 – 2x – 5 4x2 + 20x + 25.

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Presentation transcript:

Warm – Up # 9 Factor the following: 3x2 – 2x – 5 4x2 + 20x + 25

Solving Quadratic Equations What happens when we solve for x after we factor a trinomial?

Vocabulary: Quadratic Equation – any equation where 2 is the highest exponent. Standard form of a quadratic equation -

The solutions(roots) of the equation are 3 and - 6 The zero-product law is used to solve an equation when one side is zero and the other side is a product of polynomial factors For example: m · n = 0, then m = 0 or n = 0. The solutions of such an equation are also called roots. Example: (x-3)(x+6) = 0 X - 3 = 0 or x + 6 = 0 X = 3 or x = - 6 The solutions(roots) of the equation are 3 and - 6

Examples: (k + 1)(k – 5) = 0 (a + 1)(a + 2) = 0 (4k + 5)(k + 1) = 0 4. (2m + 3)(4m + 3) = 0

Solve an equation by factoring: 6x2 + 12x = 0 6x2 + 12x = 0 (Write the original equation) 6x(x + 2) = 0 (Factor left side) 6x = 0 or x + 2 = 0 (Zero-product property) X = 0 or x = - 2 (Solve for x) The solutions of the equation are 0 and – 2.

Practice 1. b2 + 14b = 0 2. 24k2 + 24k = 0

Examples: 1. 2. 3.

What if we have a problem that looks like this… What should we do??

Or like this… 9p2 -36 = 0

~ Review~ 1. 4. 2. 3.