^ Challenge 47. Consider the graphs of y = ax2 and y = (ax)2. Assume a 0.
a. For what values of a will both graphs lie in the same quadrant(s)?
b. For what values of a will the graph of y = ax2 be wider than the graph of y = (ax)2?- Reasoning Complete each statement. Assume a + 0.
a. The graph of y = ax2 + c intersects the x-axis in two places when ?•
b. The graph of y = ax2 + c does not intersect the x-axis when?. - Construction A blueprint for a 15 ft-by-9 ft rectangular wall has a square window
in the center. If each side of the window is x feet, the function y = 135 - x2 gives
the area (in square feet) of the wall without the window.
a. Graph the function.
b. What is a reasonable domain for the function? Explain.
c. What is the range of the function? Explain.
d. Estimate the side length of the window if the area of the wall is 117 ft2.
St a n d a r d i ze d Test Pr ep
A^SAT/ACT 50. Which equation has a graph that is narrower than the graph of y = 4x2 + 5?Sh o r t
Resp o n seCD y = 4x2 - 5
CD y= -5x2 + 4CO y = 0.75x + 5
CD y= -0.75x2-451. Kristina is evaluating some formulas as part of a science experiment. One of the
formulas involves the expression 24 — (—17). What is the value of this expression?
CO -41 CO -7- Which expression is equivalent to 8(x + 9)?
CO x + 72 C D 8x + 72
CH>7CO 8x + 17- What is the solution of the equation 2(x + 3) + 7 = —11?
CD-12 CO-1 CEDI
CD 41CO 8x + 9CD 12
- A rectangular dog run has an area of x2 - 22x - 48. What are possible dimensions
of the dog run? Use factoring. Explain how you found the dimensions.
Mixed Review
Factor completely.- 30r3 + 51r2 + 9r 56. 15q3 - 18 q2 - 1()q + 12
Get Read y! To p r e p a r e f o r Lesso n 9 - 2 , d o Ex er ci ses 5 8 - 6 3.
Evaluate the expression ^ for the following values of a and b.- a = —2, b = 3 59. a = —5, b = — 4
- a = 10, h = —7 62. a = —4, b = 1
See Lesson 8 - 8.- lb4 + 14b3 + b + 2
See Lesson 1-6.- a = 8, b = 6
- a = —12, b = -48
5 5 2 Chapter 9 Quadratic Functions and Equations