Section 5.2 Introduction to Solving Quadratic Equations Objectives: Solve quadratic equations by taking square roots. Use the Pythagorean Theorem to solve problems involving right triangles. Standard: N. Solve quadratic equations.

Solving Equations of the Form x 2 = a If x 2 = a and a > 0, then x = or x = -, or simply x = +

I. Properties of Square Roots *** Product Property of Square Roots If a ≥ 0, and b ≥ 0: Quotient Property of Square Roots If a ≥ 0 and b ≥ 0 : =

Example 1

Example 2 * Solve 5x 2 – 19 = 231. Give exact solutions. Then give approximate solutions to the nearest hundredth.

Example 3

Example 4 * Solve 4(x+2) 2 = 49

A rescue helicopter hovering 68 feet above a boat in distress drops a life raft. The height in feet of the raft above the water can be modeled by h(t) = -16t , where t is the time in seconds after it is dropped. After how many seconds will the raft dropped from the helicopter hit the water? 68 ft When the raft hits the water, the height will = 0, so h(t) = 0: Since only positive values of time make sense, the answer is 2.1 seconds.

II. Pythagorean Theorem If ∆ABC is a right triangle with the right angle at C, then a 2 + b 2 = c 2. When you apply the Pythagorean Theorem, use the principal square root (positive square root) because distance and length cannot be negative. a b c

a. b. (5.1) 2 + (2.5) 2 = z 2 p 2 + (4) 2 = (8.2) = z 2 p 2 = = zp = 7.2 c.d. Ex 1. Find the unknown length in each right triangle. Give answers to the nearest tenth. z = ? y = 5.1 x = 2.5 r = 8.2 q = 4 p = ? z = 8.5 x = 2.5 y = ? p = 8.7 q = 3.4 r = ? y = 8.1r = 9.3

Homework Pg : #14-42 even & 52, 53, 54, 57