EXAMPLE 4 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest...
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EXAMPLE 4 Solve a quadratic equation ve 6(x – 4) 2 = 42. Round the solutions to the neare dredth. 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 tions are 4 + 6.65 and 4 – 1 7 7
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Transcript of EXAMPLE 4 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest...
EXAMPLE 4 Solve a quadratic equation
Solve 6(x – 4)2 = 42. Round the solutions to the nearesthundredth.
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 4 + 6.65 and 4 – 1.35.7 7
Solve a quadratic equation
EXAMPLE 4
CHECKTo 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 1Use 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 = – 16t2 + vt + s Vertical motion model
h = – 16t2 + 0t + 45 Substitute for v and s.
STEP 2Find the amount of time the ball is in the air by substituting 17 for h and solving for t.
Solve a multi-step problemEXAMPLE 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 = – 16t2 + 45
17 = – 16t2 + 45
– 28 = – 16t2
28 16
= t2
28 16
= t
1.32 t
Solve a multi-step problemEXAMPLE 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.
10. 2(x – 2)2 = 18
GUIDED PRACTICE for Examples 4 and 5
ANSWER –1, 5
11. 4(q – 3)2 = 28 ANSWER 0.35, 5.65
12. 3(t + 5)2 = 24 ANSWER –7.83, –2.17
EXAMPLE 1 Solve quadratic equationsGUIDED 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 nearesthundredth of a second.
13.
ANSWER
The ball is in the are for about 1.70 second.
