Free Printable Algebra 2: Topic 2 Review

1.

Which point is the vertex?

a)

(-8, 0)

b)

(-5, -9)

c)

(-2, 0)

d)

(-9, -5)

2.

Define Axis Of Symmetry

a)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

b)

Where the parabola touches or intersects the x-axis, also called the x-intercept

c)

The highest y-value on the graph

d)

The highest or lowest point on the graph

3.

Use the picture to find the vertex and axis of symmetry

a)

Vertex (3,8) Axis x = 3

b)

Vertex (3,8) Axis y = 3

c)

Vertex (8,3) Axis x = 3

d)

Vertex (8,3) Axis y = 3

4.

What is another name for the x-intercepts of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

5.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

all real numbers

6.

Describe the transformations below: $\left(x+1\right)^2-4$

a)

left: 1, up: 4

b)

left: 1, down: 4

c)

right: 1, up: 4

d)

right: 4, up: 1

7.

Determine the vertex from the following equation: $\frac{1}{2}\left(x+4\right)^2+1$

a)

Vertex: (-4, 1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, 1)

d)

Vertex: (4, -1)

8.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

9.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

10.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

11.

Does the equation open or or down?
Y = -3x² +7x - 2

a)

up

b)

down

12.

Find the Vertex of the following Quadratic Function:

$y=x^2+12x+20$

a)

$\left(-6,-16\right)$

b)

$\left(6,-16\right)$

c)

$\left(0,20\right)$

d)

$\left(-10,0\right)$

e)

$\left(-2,0\right)$

13.

Which is the graph of the quadratic equation shown?

a)

A

b)

B

c)

C

d)

D

14.

Which is the graph the quadratic equation shown?

a)

A

b)

B

c)

C

d)

D

15.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

16.

Factor:
x² + 2x - 24

a)

(x - 6)(x + 4)

b)

(x + 6)(x + 4)

c)

(x - 6)(x - 4)

d)

(x + 6)(x - 4)

17.

Factor: 5x² - 6x - 8

a)

(5x + 1)(x - 8)

b)

(5x + 8)(x - 1)

c)

(5x + 2)(x - 4)

d)

(5x + 4)(x - 2)

18.

Factor: 3x² - 10x + 8

a)

(3x - 2)(x - 4)

b)

(3x - 4)(x - 2)

c)

(3x - 4)(x + 2)

d)

(3x + 4)(x - 2)

19.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

20.

Factor 4y² – 9.

a)

(2y + 3)(2y – 3)

b)

prime

c)

(2y + 3)(2y + 3)

d)

(2y – 3)(2y – 3)

21.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

22.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

23.

Solve the following quadratic equation by factoring:

$x^2-4x=21$

a)

$x=-4,\ 21$

b)

$x=-3,\ 7$

c)

$no\ real\ solutions$

d)

$x=-7,\ 3$

24.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

25.

a)

10

b)

-10

c)

10i

d)

-10i

26.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

27.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

28.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

29.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

30.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

31.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

32.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

33.

a)

b)

c)

d)

34.

a)

b)

c)

d)

35.

Solve by taking square roots.

x² = -121

a)

± 11

b)

± 11i

c)

± 12

d)

11i

36.

Solve using the quadratic formula...

9x² = 4 + 7x

a)

b)

c)

d)

No solution

37.

$2y^2+2=9y$

a)

$\frac{-9\pm\sqrt{65}}{2}$

b)

$\frac{9\pm5\sqrt{13}}{4}$

c)

$\frac{9\pm\sqrt{65}}{4}$

d)

$\frac{-9\pm\sqrt{-97}}{4}$

38.

$x^2-6x+4=0$

a)

$3\pm\sqrt{5}$

b)

$\frac{6\pm\sqrt{20}}{2}$

c)

$3\pm\sqrt{20}$

d)

$3\pm i\sqrt{13}$

39.

Solve the following equation. Write your answers in simplest radical form.

$x^2+10x+35=0$

a)

$-5\pm2i\sqrt{5}$

b)

$-5\pm i\sqrt{5}$

c)

$-5\pm2i\sqrt{10}$

d)

$-5\pm i\sqrt{10}$

Algebra 2: Topic 2 Review

Total questions: 39

Worksheet time: 4hrs 49mins

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