EXAMPLE 4 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x –

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EXAMPLE 4 Solve a quadratic equation 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 

Solve a quadratic equation 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.

Solve a multi-step problem 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

Solve a multi-step problem 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

Solve a multi-step problem EXAMPLE 5 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.

Solve a multi-step problem 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

Solve a multi-step problem EXAMPLE 5 ANSWER The ball is in the air for about 1.32 seconds

EXAMPLE 1 Solve quadratic equations Solve the equation. Round the solution to the nearest hundredth if necessary (x – 2) 2 = 18 GUIDED PRACTICE for Examples 4 and 5 ANSWER –1, (q – 3) 2 = 28 ANSWER 0.35, (t + 5) 2 = 24 ANSWER –7.83, –2.17

EXAMPLE 1 Solve quadratic equations GUIDED PRACTICE for Examples 4 and 5 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.