Free Printable Quadratics Test Review

1.

What is the first step in solving by completing the square?
$b^2-10b+21=0$

a)

Subtract 21 from each side of the equation.

b)

Add 21 to each side of the equation.

c)

Divide -10 by 2, square it, and then add 25 to each side.

d)

Divide -10 by 2, square it, and then subtract 25 from each side.

2.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

3.

Which line contains a mathematical error when completing the square?

a)

Line 1

b)

Line 2

c)

Line 3

d)

Line 4

e)

There is no error

4.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

5.

Simplify

$\sqrt[]{-25}$

a)

5

b)

-5

c)

5i

d)

-5i

6.

Simplify √-45

a)

3i√5

b)

-3i√5

c)

-i√45

d)

45i

7.

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

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

8.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

9.

Multiply

$\left(4i+1\right)\left(4i-1\right)$

a)

$-17+8i$

b)

$16i-1$

c)

$-17$

d)

$15$

10.

a)

10

b)

-10

c)

10i

d)

-10i

11.

(8 + 3i) + (-6 - 12i)

a)

14 + 15i

b)

14 - 9i

c)

2 - 15i

d)

2 - 9i

12.

(5 - 9i) - (1 + 4i)

a)

4 - 5i

b)

6 - 5i

c)

4 - 13i

d)

5 - 13i

13.

(9 + 5i)(4 - 2i)

a)

26 - 2i

b)

46 + 2i

c)

46 - 2i

d)

36 + 2i

14.

$6x^2-19x=-8x^2-6$

a)

$\left\{\frac{6}{7},\frac{1}{2}\right\}$

b)

$\left\{7,12\right\}$

c)

$\left\{-7,-12\right\}$

d)

$\left\{-\frac{1}{2},-\frac{6}{7}\right\}$

15.

$9x^2-12x+4=0$

a)

$\left\{6\right\}$

b)

$\left\{\frac{2}{3}\right\}$

c)

$\left\{-6,6\right\}$

d)

$\left\{\pm\frac{2}{3}\right\}$

16.

$5x^2-12=17x$

a)

$\left\{-3,20\right\}$

b)

$\left\{-\frac{3}{5},\ 4\right\}$

c)

$\left\{-4,\ \frac{3}{5}\right\}$

d)

$\left\{-20,3\right\}$

17.

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

18.

Solve

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

19.

Solve by factoring:

3x² - 11x + 6 = 0

a)

x = -2/3 and x = -3

b)

x = -1/3 and x = 6

c)

x = -3/2 and x = 3

d)

x = 2/3 and x = 3

20.

Solve:

$\left(x+3\right)^2-5=116$

a)

x = 8, x = -14

b)

No Solution

c)

$x=\pm15$

21.

$\left(x-1\right)^2=16$

a)

x = 10, 1

b)

x = 5, -3

c)

x = 4, -7

22.

$3\left(x-8\right)^2=75$

a)

x = 13, 3

b)

x = 0, -15

c)

No Solution

23.

Solve by taking square roots:
5m² + 1 = 6

a)

m = 0

b)

m = 1 or -1

c)

m = √7

d)

m = 7/5 m = -7/5

24.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

25.

Solve 2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

26.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

27.

The quadratic parent function $f\left(x\right)\ =\ x^2$ has been transformed by shifting it right three units and down 7 units. Which is the next function definition?

a)

$f\left(x\right)\ =\ \left(x+3\right)^{2\ }-\ 7$

b)

$f\left(x\right)\ =\ \left(x-3\right)^{2\ }-\ 7$

c)

$f\left(x\right)\ =\ \left(x+3\right)^{2\ }+\ 7$

d)

$f\left(x\right)\ =\ \left(x-3\right)+\ 7$

28.

What is the vertex of the quadratic function shown?

a)

(1, -4)

b)

(-2, -5)

c)

(-1, -4)

d)

(2, -5)

29.

What are the transformations?

y=(x-2)²+4 (Choose ALL that apply.)

a)

shift right 2

b)

shift left 2

c)

shift up 4

d)

shift down 4

30.

Describe the transformation: y=-3(x-2)²-4.

*Mark all that apply.

a)

reflection across x-axis

b)

VS by factor of 3

c)

VC by factor of 3

d)

down 4

e)

right 2

31.

Write the equation of this transformation: reflection across x-axis, left 2, down 5

a)

y= -(x+2)²+5

b)

y= -(x+2)²

c)

y= (x-2)²-5

d)

y= -(x+2)²-5

32.

Describe the transformation below: $-3\left(x+4\right)^2-1$

a)

stretch by 3, right: 4, down: 1

b)

reflect over the x-axis, right: 4, down: 1

c)

reflect over the x-axis, stretch by 3, left: 4, down: 1

d)

stretch by 4, down: 3, left: 1

33.

Determine the vertex from the following equation: $-3\left(x-4\right)^2+1$

a)

Vertex: (4,1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, -1)

d)

Vertex: (-4, 1)

34.

Determine the axis of symmetry of the following equation: $\left(x-3\right)^2+5$

a)

A. O. S: 1

b)

A. O. S: -3

c)

A. O. S: 3

d)

A. O. S: 5

Quadratics Test Review

Total questions: 34

Worksheet time: 38mins

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