Thinking Mathematically Algebra: Equations and Inequalities 6.6 Solving Quadratic Equations

Definition of a Quadratic Equation A quadratic equation in x is an equation that can be written in the general form ax 2 + bx + c = 0, where a, b, and c are real numbers, with a≠0. Linear vs. quadratic

Using the FOIL Method to Multiply Binomials (ax + b)(cx +d) = axcx + axd + bcx + bd = acx 2 + (ad + dc)x + bd F: First terms (x 2 term) O: Outside terms (x term) I: Inside terms (x term) L: Last terms (constant term) An application of the Distributive Property

Example: Multiplying Binomials Exercise Set 6.6 #3 (x - 5)(x + 3)

Factoring a Trinomial  The inverse of FOIL Exercise Set 6.6 #11, #13, #17, #21 x 2 -2x - 15 x 2 – 8x + 15 x 2 – 8x x 2 + 7x + 3

The Zero-Product Principle If the product of two factors is zero, then one (or both) of the factors must have a value of zero. If AB = 0, then A = 0 or B = 0. Solution set contains two answers.

Solving a Quadratic Equation Using the Zero-Product Principle Exercise Set 6.6 #33 (x – 8)(x + 3) = 0

Using Factoring to Solve a Quadratic Equation Exercise Set 6.6 #37, 41 x 2 + 8x + 15 = 0 x 2 – 4x = 21

Thinking Mathematically Algebra: Equations and Inequalities 6.6 Solving Quadratic Equations