1. Warm-Up Exercises Find the exact value. ANSWER 7 1. 49 2. – 144 ANSWER 12 – Use a calculator to approximate the value of to the nearest tenth. 3. 16 82 ANSWER 2.3

2. Example 1 Use Properties of Square Roots Simplify the expression. a. 18 b. 2 18 c. 9 5 SOLUTION 9 a. 18 = 2 = 2 3 c. 9 5 5 9 == 5 3 4 b. = = 5 2 1020 = 5 2

3. Example 2 Rationalize the Denominator of a Fraction Simplify. 2 5 SOLUTION 2 5 5 2 = Quotient property of square roots 5 2 = 2 2 2 2 Multiply by. = 10 2 Simplify.

4. Checkpoint Simplify the expression. 1. Use Properties of Square Roots 12 2. 3 15 3. 3 7 ANSWER 3 2 5 3 21 3

5. Example 3 Solve a Quadratic Equation Solve. = x 2x 2 +113 Subtract 1 from each side. = 12x 2x 2 SOLUTION = x 2x 2 +113 Write original equation. = x + – 12 Take the square root of each side. = x + – 43 Product property of square roots = x + – 32 Simplify. ANSWER The solutions are and. 32 32 –

6. Example 3 Solve a Quadratic Equation CHECK 32 32 – Substitute and into the original equation. = x 2x 2 +113 = x 2x 2 +1 +1 = ? 43 +113 = ? 43 = 12+113 = 12+113 +1 32()2)2 = ? +1 = ? 32()2)2 –

7. Checkpoint Solve the equation. Solving a Quadratic Equation 4. = x 2x 2 4 – 14 5. = x 2x 2 313+ ANSWER 2,2, 3 23 – 10, 10 – = 3y 23y 2 24 6. ANSWER 2,2, 2 22 –

8. Example 4 Use a Quadratic Equation as a Model Skydiving A skydiver jumps from an airplane that is 6000 feet above the ground. The skydiver opens her parachute when she is 2500 feet above the ground. a.Write an equation that gives the height (in feet) of the skydiver above the ground as a function of time (in seconds). b. For how many seconds does the skydiver fall before opening her parachute? SOLUTION a. The initial height of the skydiver is h 0 6000. = Write falling object model. – = 16t 2 h + h0h0

9. Example 4 Use a Quadratic Equation as a Model Substitute 6000 for h 0. – = 16t 2 h + 6000 b. The height of the skydiver when she opens her parachute is h 2500. Substitute 2500 for h in the model from part (a). Solve for t. = Write model from part (a). – = 16t 2 h + 6000 Substitute 2500 for h. – = 16t 2 2500 + 6000 Subtract 6000 from each side. – = 16t 2 3500 – Divide each side by 16. t 2t 2 = 16 3500 – – –

10. Example 4 Use a Quadratic Equation as a Model Take the square root of each side. t = 16 3500 – – – + Use a calculator. – + t ≈ 15 ANSWER Reject the solution 15, because time must be positive. The skydiver falls for about 15 seconds before opening her parachute. –

11. Checkpoint 7. Skydiving A skydiver jumps from a plane that is 5000 feet above the ground. The skydiver opens his parachute when he is 2000 feet above the ground. Use a Quadratic Equation a. Write an equation that gives the height (in feet) of the skydiver above the ground as a function of time (in seconds). ANSWER – = 16t 2 h + 5000 b. For how many seconds does the skydiver fall before opening his parachute? ANSWER about 14 sec