8-32.Without Graphing, Determine Where the Graph Off(X) =X2+ 6X+ 14 Intersects Thex-Axis

Name: ______Date: ______

HW IM3 8.1.2-8.1.3Block: ____

8-32.Without graphing, determine where the graph off(x) =x2+ 6x+ 14 intersects thex-axis. Justify your answer.

8-33.For each set of points given below, write a possible equation for a quadratic function in standard form.

1. (–3, 0) and,

8-34.What is the degree of each polynomial function below? For parts (c) and (d), state the minimum degree.

a. P(x) = 0.08x2+ 28xb. y= 8x2–x5+ 9

c. d.

8-35.Consider the following types of graphs. Which graphs are polynomial functions? Explain your reasoning.

a. parabolas

b. exponentials

c. cubics

d. lines

e. circles

8-36.The graph of an exponential functiony=abx+kpasses through (3,7.5) and (4,6.25). It also has an asymptote aty=5.

a. What is the equation of the function?

b. If the function also passes through (8,w), what is the value ofw?

8-38.Solve the system of equations below.

x2+y2=16
y=x2–4

8-48.Write a polynomial equation for a graph that passes through the point (–1,60) and has threexintercepts: (–4,0), (1,0), and (3,0).

8-49.Consider the quadratic equationx2– 10x= –29.

1. Isx= 5 + 2ia solution to the equation? How can you be sure without solving?

1. Without solving, predict another solution to the equation. Verify your prediction by checking it.

1. Where does the parabolay=x2– 10x+ 29 intersect thexaxis? Explain.

8-50.For each of the following polynomial functions, state the degree, list the coefficients, and then label thema0throughan. Refer to the example in the Math Notes box in Lesson 8.1.1 about polynomial notation.

a. P(x) = 6x4– 3x3+ 5x2+x+ 8

b. P(x) = –5x3+ 10x2+ 8

c. P(x) = –x2+x

d. P(x) =x(x– 3)(x– 5)

e. P(x) =x

f. P(x) = 10

8-51Solve each of the following equations.

b. 2x+ 3 = 10

8-52.Deniz’s computer is infected with a virus that will erase information from her hard drive. It will erase information quickly at first, but as time goes on, the rate at which information is erased will decrease. Intminutes after the virus starts erasing information, 5,000,000bytes of information remain on the hard drive.

1. Before the virus starts erasing, how many bytes of information are on Deniz’s hard drive?

1. After how many minutes will there be 1000 bytes of information left on the hard drive?

1. When will the hard drive be completely erased?

8-53.Calculate the length of the missing side in each triangle below. Write your answers in exact form.

a. / / c. /

8-54.Solve and graph the inequality.

b. 3− 1 > 8