1. Solve quadratic equations
EXAMPLE 1
Solve quadratic equations
Solve the equation.
a. 2x2 = 8
SOLUTION
a. 2x2 = 8
Write original equation.
x2 = 4
Divide each side by 2.
x = ± 4 = ± 2 
Take square roots of each side.
Simplify.
The solutions are –2 and 2.
ANSWER

2. Solve quadratic equations
EXAMPLE 1
Solve quadratic equations
b. m2 – 18 = – 18
Write original equation.
m2 = 0
Add 18 to each side.
m = 0
The square root of 0 is 0.
ANSWER
The solution is 0.

3. Solve quadratic equations
EXAMPLE 1
Solve quadratic equations
c. b = 5
Write original equation.
b2 = – 7
Subtract 12 from each side.
ANSWER
Negative real numbers do not have real square roots.
So, there is no solution.

4.  EXAMPLE 2 Take square roots of a fraction Solve 4z2 = 9. SOLUTION
Write original equation.
z2 = 9 4
Divide each side by 4.
z = ±  9 4
Take square roots of each side.
z = ± 3 2
Simplify.

5. EXAMPLE 2
Take square roots of a fraction
ANSWER
The solutions are – and 3 2

6. Approximate solutions of a quadratic equation
EXAMPLE 3
Approximate solutions of a quadratic equation
Solve 3x2 – 11 = 7. Round the solutions to the nearest
hundredth.
SOLUTION
3x2 – 11 = 7
Write original equation.
3x2 = 18
Add 11 to each side.
x2 = 6
Divide each side by 3.
x = ± 6 
Take square roots of each side.

7. Approximate solutions of a quadratic equation
EXAMPLE 3
Approximate solutions of a quadratic equation
x ± 2.45
Use a calculator. Round to the nearest
hundredth.
ANSWER
The solutions are about – 2.45 and about 2.45.

8. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
for Examples 1,2 and 3
Solve the equation.
1. c2 – 25 = 0
w = – 8
x = 11

9. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
for Examples 1,2 and 3
Solve the equation.
x2 = 16
m2 = 100
b = 0

10. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
for Examples 1,2 and 3
Solve the equation. Round the solutions to the nearest hundredth.
7. x2 + 4 = 14
k2 – 1 = 0
p2 – 7 = 2

11. Solve a quadratic equation
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 

12. EXAMPLE 4
Solve a quadratic equation
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.

13. EXAMPLE 5
Solve a multi-step problem
SPORTS EVENT
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.

14. EXAMPLE 5
Solve a multi-step problem
SOLUTION
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).

15. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
h = – 16t2 + vt + s
Vertical motion model
h = – 16t2 + 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.

16.  EXAMPLE 5 Solve a multi-step problem h = – 16t2 + 45
Write model.
17 = – 16t2 + 45
Substitute 17 for h.
– 28 = – 16t2
Subtract 45 from each side. 28 16
= t2
Divide each side by 16.  28
= t
Take positive square root. 16 t
Use a calculator.

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

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

19. EXAMPLE 1
GUIDED PRACTICE
Solve quadratic equations
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.