10.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Square Roots to Solve Quadratic Equations
10.4 Warm-Up Evaluate the expression. ANSWER –7 ANSWER about – 49√ √ 3.± 121√ ANSWER ±11
10.4 Warm-Up ANSWER 0.75 sec A ball is dropped from a height 9 feet above the ground. How long does it take the ball to hit the ground? 4.
10.4 Example 1 Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ± 4 = ± 2 Take square roots of each side. Simplify. The solutions are –2 and 2. ANSWER b. m 2 – 18 = – 18 c. b = 5
10.4 Example 1 b. m 2 – 18 = – 18 Write original equation. m 2 = 0 Add 18 to each side. The square root of 0 is 0. m = 0m = 0 ANSWER The solution is 0.
10.4 Example 1 c. b = 5 Write original equation. b 2 = –7 Subtract 12 from each side. ANSWER Negative real numbers do not have real square roots. So, there is no solution.
10.4 Example 2 Solve 4z 2 = 9. SOLUTION 4z 2 = 9 Write original equation. z 2 = 9 4 Divide each side by 4. Take square roots of each side. z = ± Simplify. The solutions are – and ANSWER
10.4 Guided Practice Solve the equation. 1. c 2 – 25 = 0 ANSWER –5, w = – 8 ANSWER no solution 3. 2x = 11 ANSWER x 2 = 16 ANSWER –, 5. 9m 2 = 100 ANSWER 10 3 –, b = 0 ANSWER no solution
10.4 Example 3 Solve 3x 2 – 11 = 7. Round the solutions to the nearest hundredth. SOLUTION 3x 2 – 11 = 7 Write original equation. 3x 2 = 18 Add 11 to each side. x 2 = 6 Divide each side by 3. x = ± 6 Take square roots of each side. x ± 2.45 Use a calculator. Round to the nearest hundredth. ANSWER The solutions are about – 2.45 and about 2.45.
10.4 Guided Practice Solve the equation. Round the solutions to the nearest hundredth. 7. x = 14 ANSWER – 3.16, k 2 – 1 = 0 ANSWER – 0.58, p 2 – 7 = 2 ANSWER – 2.12, 2.12
10.4 Example 4 Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x – 4) 2 = 7 Divide each side by 6. x – 4 = ± 7 Take square roots of each side. 7 x = 4 ± Add 4 to each side. ANSWER The solutions are and 4 – 7
10.4 Example 4 CHECK To check the solutions, first write the equation so that 0 is on one side as follows: 6(x – 4) 2 – 42 = 0. Then graph the related function y = 6(x – 4) 2 – 42. The x -intercepts appear to be about 6.6 and about 1.3. So, each solution checks.
10.4 Guided Practice Solve the equation. Round the solution to the nearest hundredth if necessary (x – 2) 2 = 18 ANSWER –1, (q – 3) 2 = 28 ANSWER 0.35, (t + 5) 2 = 24 ANSWER –7.83, –2.17
10.4 Example 5 During an ice hockey game, a remote-controlled blimp flies above the crowd and drops a numbered table-tennis ball. The number on the ball corresponds to a prize. Use the information in the diagram to find the amount of time that the ball is in the air. SPORTS EVENT
10.4 Example 5 STEP 1 Use the vertical motion model to write an equation for the height h (in feet) of the ball as a function of time t (in seconds). SOLUTION h = –16t 2 + vt + s Vertical motion model h = –16t 2 + 0t + 45 Substitute for v and s. STEP 2 Find the amount of time the ball is in the air by substituting 17 for h and solving for t.
10.4 Example 5 Write model. Substitute 17 for h. Subtract 45 from each side. Divide each side by 16. Take positive square root. Use a calculator. h = –16t = –16t – 28 = –16t = t 2 = t 1.32 t ANSWER The ball is in the air for about 1.32 seconds
10.4 Guided Practice WHAT IF? In Example 5, suppose the table-tennis ball is released 58 feet above the ground and is caught 12 feet above the ground. Find the amount of time that the ball is in the air. Round your answer to the nearest hundredth of a second. 13. ANSWER The ball is in the are for about 1.70 second.
10.4 Lesson Quiz ANSWER –2, 2 Solve the equation. Round solutions to the nearest hundredth, if necessary. 1. 4b 2 – 13 = x 2 = 25 ANSWER –3.16, 3.16 ANSWER – , 3. 3n 2 –18 = 12
10.4 Lesson Quiz At a football game you are sitting 32 feet above the ground. If your hat comes off and falls to the ground, how long will it be in the air ? 4. ANSWER About 1.41 sec