Chpt 9 new algebra Version 1
Name:______Date:______
1.)Graph the following inequalities on separate axes.a. b.
2.)Tamara’s little brother, Zane, likes to throw his baseball cap over the fence in their backyard. The motion of the cap is represented by the equation , where x represents the number of seconds after Zane threw his cap in the air, and y represents the vertical height of the cap with respect to the ground (assume that the cap is on the ground before Zane picks it up to throw it).
a.How long is the cap in the air? How can you tell?
b.At what time does the cap stop going up and start coming down?
c.If Zane has a 6-foot fence in his backyard, will his cap make it over the top? How do you know?
d.Draw a sketch of the graph representing the motion of Zane’s cap. Label all the important points with coordinates and words that tell what the points mean in this situation.
3.)Solve .
4.)Solve each inequality. Show your solution algebraically and on a number line.
a.b.
c.
5.)Holly plays tennis on the school tennis team. She can hit a tennis ball really high in the air. She learned that the quadratic equation y = –6x2 + 36x could be used to determine the height of a tennis ball after it was hit with a tennis racket (y = the height of the tennis ball in feet, x = seconds after the ball is hit with the racket).
a.How long does it take for the ball to hit the ground? How can you tell?
b.What is the highest point reached during the flight of the ball? How do you know?
c.When was the ball exactly 48 feet off the ground? Explain your reasoning.
6.)What are the roots of each equation below? Use factoring, if possible.
a.b.
c. d.
7.)Find the x- and y-intercepts for the rule y = (x–6)(x + 3) without making a table or graphing.
8.)Use the Zero Product Property to find the roots of the quadratic equations below.
a.b.c.
9.)Solve each of the following equations for x. Show all your work.
a.x2 + 6x + 8 = 0b.3x2 + 6x = 0
10.)Decide whether each of the following points is on the graph of y = –2x2 + 5x – 1. Explain how you know.
a.(–2, –19)b.(2, 19)
11.)Write an inequality that represents the solutions on the number lines below.
a. b.
12.)Examine the graph below.
a.Write an inequality for the graph.
b.Give as much information as you can about the solution for the inequality.
13.)Graph the inequalities below on graph paper.
a.b.
14.)Multiple Choice: Select the correct inequality to match the graph at right. Show your reasoning.
A.
B.
C.
D.
15.)Draw a graph of the solution region for the system of inequalities below.
16.)Factor each expression below.
a.9x2 + 24 + 16y2b.x3 + 4x2 + 4x
17.) Factor each of the following completely.
a.16x2 – 4
b.81y2 – 100
c.45a2 – 125