Algebra 1 Chapter 8 Review

Characteristics

100

Are the following functions quadratic?

a. y = 2x²+9x-5

b. y = -4x+3

c. y = 3x³+2x²+x

a. yes

b. No

c. No

200

Tell wether the following functions open up or down: 

a. y = 5x²-12

b. y = -x²+3x-7

c. y+x²=x

a. up

b. down

c. down

300

Find the zeros and the max/min from the graph of y=2x²-4x-6. Also find the y- intercept. (See graph on PDF)

Zeros at: x = -1 and x = 3

Min = -8

y-intercept: (0,-6)

400

Find the vertex and the axis of symmetry of the following graph. (See Graph on PDF)

Axis: x = -1

Vertex: (-1,5)

500

Find the domain and range of the following graph: 

y = x²+6x+6

(See Graph on PDF)

D: {R}

R: {y>-3}

Transformations

100

Order the graphs by width from narrowest to widest. 

f(x)=2x²

g(x)= -4x²

g(x), f(x)

200

Order the graphs by width from narrowest to widest. 

f(x) = x²

g(x) = 1/3x²

h(x)= 3x²

h(x), f(x), g(x)

300

Compare g(x)= x²+5 with the graph of f(x)=x²

opens up, same width, translates up 5

400

Compare g(x)= 3x²-1 with the graph of f(x)=x²

opens up, narrower, translates down 1.

500

Compare g(x)= -1/2x²+3 with the graph of f(x)=x²

Opens down, wider, Translates up 3

Graphing Quadratics

100

Find the axis of symmetry of the following: 

y = 5x² - 20x + 25

x = 2

200

Find the Vertex of the following: 

y = -4x² - 16x - 10

(-2, 6)

300

Graph the following: 

y = -x² + 2x + 8 

See Graph on PDF. 

400

Graph the following: 

y = 3x² + 6x - 2

See Graph on PDF. 

500

Graph the following: 

y = -x² - 4

See Graph on PDF.

Word Problems

100

What is the vertical motion model?

h(t) = -16t² + v₀t+ h₀

200

1. The height h in feet of a projectile launched vertically upward at an initial vertical velocity of 80 ft/s  from the top of a 96-foot tall tower when time t=0 is given by what equation?

h(t) = -16t² + 80t + 96

300

The height h in feet of a projectile launched vertically upward at an initial vertical velocity of 80 ft/s  from the top of a 96-foot tall tower when time t=0 is given by h(t) = -16t² + 80t + 96. What is the max height it will reach?

196 feet

400

While playing catch yesterday with his grandson, Tim throws a ball as hard as possible into the air. The height h in feet of the ball is given by h=-16t²+64t+8, where t is in seconds.What is the maximum height of the ball? How long does it take to reach the maximum height?

Max Height: 72 feet

Time to reach Max Height: 2 seconds

500

One edge of a painting is 6 in. longer than the shorter edge. The picture has a 2-in.-wide frame. Write a quadratic function to represent the area of the picture and the frame. Find the area if the short edge is 8 inches long. 

f(x) = x² + 14x + 40

Area: 216 in²