Free Printable Alg 1: Ch 8-9 Review

1.

Choose the correct graph of

$f\left(x\right)\ =\ x^2+3$

a)

b)

c)

d)

2.

Choose the correct graph of

$f\left(x\right)\ =\ -x^2-2.5$

a)

b)

c)

d)

3.

Graph (You need to accurately plot the vertex, and then plug in x = 1 to plot another point. On the test, remember that you will need to make a table for both x = 1 and x = 2!:

$f\left(x\right)\ =\ -2x^2-1$

4.

Choose the correct graph of

$f\left(x\right)\ =\ -\frac{1}{4}x^2+3$

a)

b)

c)

d)

5.

What is the domain of the function?
*Hint: Domain is the set of all x-values included in the function.

a)

x≥3

b)

x≤3

c)

All real numbers

d)

-1≤x≤5

6.

What is the range of the function?
*Hint: Range is all of the y-values included in the function.

a)

y≤3

b)

y≥3

c)

All real numbers

d)

-6≤y≤3

7.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

8.

The solutions of a quadratic equation are known as the _____.

a)

Vertices

b)

Roots

c)

Squares

d)

Formulas

9.

a)

A
1 Real Solution

b)

B
2 Real Solutions

c)

C
No Real Solutions

d)

D
Half a Solution

10.

How many solutions would this quadratic equation have?

a)

A

No Real Solutions

b)

B

One Real Solution

c)

C

Two Real Solutions

d)

D

Four Real Solutions

11.

What is another name for the solutions to a quadratic?

a)

A

y-intercepts

b)

B

Zeros

c)

C

Maximums

d)

D

Minimums

12.

What are the solutions to this function?

a)

x={2}

b)

x={2,0}

c)

x={-2}

d)

x={0,-2}

13.

x²=25

a)

x = 5

b)

x = -5

c)

x = ±25

d)

x = ±5

14.

(x + 3)² = 36

a)

x = √36

b)

x = √39

c)

x = -9 and x = 3

d)

x = 9 and x = -3

15.

Solve by taking square roots:

5m² + 1 = 6

a)

m = 1

b)

m = 1 or -1

c)

m = √7

d)

m = 7/5 m = -7/5

16.

Solve using square roots.

k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no real solution

17.

Use the square root property to solve the Quadratic Equation.
2(x - 4)² = 200

a)

±10

b)

-14, 6

c)

-6, 14

d)

100

18.

Solve by taking square roots.

x² +12 = 5

a)

x = ± 49

b)

No Real Solutions

c)

x = ± √7

d)

x = ± 5/12

19.

What is name of the graph of a Quadratic Equation?

a)

Line

b)

Parbola

c)

U

d)

Parabola

20.

Solve using the Quadratic Formula:
(Hint: Set the equation = to 0)

$x^2+4x-40=-8$

a)

$x=-10,\ -4$

b)

$x=-4,\ 10$

c)

$x=-8,\ 4$

d)

$x=-4,\ 8$

21.

Solve using the Quadratic Formula:

$2x^2-x-3=0$

a)

$x=-\frac{3}{2},\ 1$

b)

$x=-1,\ \frac{3}{2}$

c)

$x=-\frac{3}{2},\ -1$

d)

$x=1,\ \frac{3}{2}$

22.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

23.

$7x^2=6x-1$

Given this quadratic equation, what could be the values a, b, and c to use in the quadratic formula?

a)

$a\ =\ 7,\ b\ =\ -6,\ c\ =\ 1$

b)

$a\ =\ 1,\ b\ =\ 6,\ c\ =\ -7$

c)

$a\ =\ -7,\ b\ =\ 6,\ c\ =\ 1$

d)

$a\ =\ 6,\ b\ =\ 7,\ c\ =\ 1$

24.

What is the color of the graph that has exactly one real zero?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs has exactly one zero.

25.

How many real solutions can a quadratic equation of the form shown have?
Check all that apply.

ax^2+bx+c=0

a)

0

b)

1

c)

2

d)

3

e)

infinitely many

26.

TRUE OR FALSE:

The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

27.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

28.

The quadratic function $y=3x^2-9$

a)

Is narrower than y=x^2 and has a vertex at (0,-9)

b)

Is narrower than y=x^2 and has a vertex at (0,9)

c)

Is wider than y=x^2 and has a vertex at (0,-9)

d)

Is wider than y=x^2 and has a vertex at (0,9)

29.

The quadratic function $f\left(x\right)=\frac{1}{3}x^2+2$

a)

Is Hill Shaped (opens down) and has a vertex at (0,2)

b)

Is U Shaped (opens up) and has a vertex at (0,2)

c)

Is Hill Shaped (opens down) and has a vertex at (2,0)

d)

Is U Shaped (opens up) and has a vertex at (2,0)

30.

The quadratic function $g\left(x\right)=-4x^2$

a)

Is U shaped (opens up) and has no vertex.

b)

Is Hill shaped (opens down) and has no vertex.

c)

Is U shaped (opens up) and has a vertex at (0,0)

d)

Is Hill shaped (opens down) and has a vertex at (0,0)

31.

The quadratic function $y=-\frac{1}{4}x^2+5$

a)

Is wider than y=x^2 and has a vertex at (0,-5)

b)

Is narrower than y=x^2 and has a vertex at (0,-5)

c)

Is wider than y=x^2 and has a vertex at (0,5)

d)

Is narrower than y=x^2 and has a vertex at (0,5)

32.

The function h(t) = -16t²+60t + 130 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4.2 seconds

b)

4.9 seconds

c)

5.3 seconds

d)

5.8 seconds

e)

6.1 seconds

33.

a)

2

b)

-2

c)

4

d)

-4

34.

Solve.

a)

8

b)

-8

c)

0

d)

no solution

35.

a)

5

b)

33

c)

85

d)

21

Alg 1: Ch 8-9 Review

Total questions: 35

Worksheet time: 2hrs 22mins

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