1. 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: 2.8.11.N. Solve quadratic equations.

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

3. 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 : =

4. Example 1

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

6. Example 3

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

8. Example 5 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 2 + 68, 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? -16t 2 + 68 = 0 68 ft

9. 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 because distance and length cannot be negative. a b c

10. a. b. (5.1) 2 + (2.5) 2 = z 2 p 2 + (4) 2 = (8.2) 2 32.26 = z 2 p 2 = 51.24 5.7 = 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

12. PSSA Warm-Up Question How can you use the Pythagorean Theorem to solve problems involving right triangles? Solve the following word problem: The base of a 30-foot ladder is 18 feet from a tree. How high up the tree does it reach?

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