Name: __________________________________________

1

Int Math 2 Review Handout (Sec.12-1 thru 12-2)

What are the coordinates of the vertex of the graph or table? Is it a maximum or minimum?

1

2

Name: ______________________ ID: A

2

Graph the function and identify the domain and range.

3 y = 1.5x2

A domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: −∞,0ÊËÁÁ

˘˚˙̇̇

C domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: 0,∞ÈÎÍÍÍ ˆ

¯̃̃

B domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: −∞,0ÊËÁÁ

˘˚˙̇̇

D domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: 0,∞ÈÎÍÍÍ ˆ

¯̃̃

Name: ______________________ ID: A

3

4 y = –0.5x2

A domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: 0,∞ÈÎÍÍÍ ˆ

¯̃̃

C domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: −∞,0ÊËÁÁ

˘˚˙̇̇

B domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: 0,∞ÈÎÍÍÍ ˆ

¯̃̃

D domain: −∞,∞ÊËÁÁ

ˆ¯̃̃

range: −∞,0ÊËÁÁ

˘˚˙̇̇

Name: ______________________ ID: A

4

Order the group of quadratic functions from widest to narrowest graph.

5 y = 4x 2, y = 5x 2, y = 3x 2

A y = 3x 2, y = 5x 2, y = 4x 2

B y = 5x 2, y = 4x 2, y = 3x 2

C y = 3x 2, y = 4x 2, y = 5x 2

D y = 4x 2, y = 3x 2, y = 5x 2

6 y = −5x 2, y = −4x 2, y = −3x 2

7 y = − 23x2, y = − 3

4x2, y = 5

4x2

8 How is the graph of y = –3x2 + 2 different from the graph of y = –3x2?

A It is shifted 2 unit(s) up. B It is shifted 2 unit(s) left.C It is shifted 2 unit(s) down. D It is shifted 2 unit(s) right.

9 How is the graph of y = 2x2 – 3 different from the graph of y = 2x2?

A It is shifted 3 unit(s) left.B It is shifted 3 unit(s) down. C It is shifted 3 unit(s) up. D It is shifted 3 unit(s) right.

10 If an object is dropped from a height of 400 feet, the function h(t) = −16t2 + 400 gives the height of the object after t seconds. When will the object hit the ground?

11 If an object is dropped from a height of 116 feet, the function h(t) = −16t2 + 116 gives the height of the object after t seconds. When will the object hit the ground?

Name: ______________________ ID: A

5

12 Graph the function. Identify the vertex and axis of symmetry.

f(x) = x 2 + 3x + 2

A axis of symmetry: x = −1.5vertex: (–1.5, 0.25)

C axis of symmetry: x = 1.5vertex: (1.5, 0.25)

B axis of symmetry: x = 1.5vertex: (1.5, –0.25)

D axis of symmetry: x = −1.5vertex: (–1.5, –0.25)

Name: ______________________ ID: A

6

13 If f(x) = x 2 + 1 and g(x) = f(2x), graph g(x) and write the equation for g(x).

A g(x) = 2x 2 + 1 C g(x) = 4x 2 + 1

B g(x) = 4x 2 + 2 D g(x) = 2x 2 + 2

Name: ______________________ ID: A

7

14 If f(x) = x 2 + 1 and g(x) = −3f(x), graph g(x) and write the equation for g(x).

15 Do the equation and graph below share a vertex? If so, what is it?

f(x) = x 2 − 6x + 4

A yes, (1, –1) C yes, ( 12

, −1 12

)

B no D yes, (3, –5)

Name: ______________________ ID: A

8

16 A ball is thrown into the air with an upward velocity of 40 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 40t + 10. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary

A 1.25 s; 35 ft B 2.5 s; 10 ft C 1.25 s; 85 ft D 1.25 s; 40 ft

17 A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = −16t2 + 112t + 30. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.