0 A p p ly @ 3 2. T h in k A b o u t a P lan A park is installing a rectangular reflecting pool surrounded by
a concrete walkway of uniform width. The reflecting pool will measure 42 ft by 26 ft.
There is enough concrete to cover 460 ft2 for the walkway. What is the maximum
width x of the walkway?
- How can drawing a diagram help you solve this problem?
- How can you write an expression in terms of x for the area of the walkway?
- Landscaping A school is fencing in a rectangular area for a playground.
It plans to enclose the playground using fencing on three sides, as shown
at the right. The school has budgeted enough money for 75 ft of fencing
material and would like to make a playground with an area of 600 ft2.
a. Let w represent the width of the playground. Write an expression in
terms of w for the length of the playground.
b. Write and solve an equation to find the width w. Round to the
nearest tenth of a foot.
c. What should the length of the playground be?
Solve each equation. If necessary, round to the nearest hundredth. If there is no
real-number solution, write no solution.- q2 + 3q + 1 = 0^ 35. s2 + 5 s = -ll 36. w2 + 7w - 4 0 = 0
- zl -8 z= -13
- 2 p2 - 15p + 8 = 43
- 4 p2 - 40p + 56 = 0
- 3r2 — 27r = 3
- m2 + 4m + 13 = — 8
- s2 + 9s + 20 = 0
4 3. E rro r A n alysis A classmate was completing the square to solve 4x2 + lO x = 8. For
her first step she wrote 4x2 + lO x + 25 = 8 + 25. What was her error?- Reasoning Explain why completing the square is a better strategy for solving
x2 - 7x - 9 = 0 than graphing or factoring. - Open-Ended Write a quadratic equation and solve it by completing the square.
Show your work.
Use each graph to estimate the values of x for which f(x) = 5. Then write
and solve an equation to find the values of x such that / ( x ) = 5. Round to the
nearest hundredth.- /(x) = x2 - 2x - 1 47. f{x) = -|x2 + 2x + 6
./ Y
(^4) V
1- \
-3
-f
/ C
580 Ch ap t er 9 Quadratic Functions and Equations