Free Printable Quadratics Review

Worksheets

Quadratics Review - Graphing & Solving

Total questions: 31

Worksheet time: 3hrs 41mins

Name

Class

Date

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

Maximum

Minimum

The axis of symmetry line passes through which point?

y-intercept

any random point

vertex

symmetrical point for the vertex

Identify the vertex and whether the graph opens up or down.

(5, 2); opens up

(5, 2); opens down

(-5, 2); opens up

(-5, 2); opens down

$y=x^2+6x+4$ What are the coordinates of the vertex?

(a)

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

(2, 3); minimum

(2, 5); maximum

(2, 3); maximum

(2, -3); minimum

(2, -3); maximum

What are the coordinates of the y - intercept?

(a)

The parabola y = x² - 2x + 4 will

open up

open down

The parabola y = - 2x² - 4x + 1 will have an axis of symmetry of

x = - 1

x = 1

x = 4

x = - 4

10.

The vertex of parabola y = - 2x² - 4x + 1 is

(1, 3)

(- 1, 3)

(- 1, -5)

(- 1, 5)

11.

Solve for x

x² = 64

x = 8, -8

x = 32, -32

x = 4, -4

No real solution

12.

Solve using square roots.
k² - 6 = 43

k = √37

k = 37 or - 37

k = 7, k = -7

no solution

13.

Solve for x

3x² - 27 = 0

x = 4.9, -4.9

x = 9, -9

x = 3, -3

No solution

14.

Solve: $x^2+8=28$

No solution

$x=\pm4\sqrt{5}$

$x=\pm6$

$x=\pm2\sqrt{5}$

15.

Simplify the square root.

16.

Simplify the square root.

17.

Solve by factoring: 2x²+ 7x + 6 = 0

x= 3/2 and x = 2

x = -3/2 and x = -2

x = 6 and x = 7

x = -6 and x = -7

18.

Select the solution(s) for the quadratic: $x^2-11x+19=-5$

-9

-3

19.

Solve by factoring: 5x² + 13x + 6 = 0

x = -2 and x = -3/5

x = 2 and x = 3/5

x = -2 and x = 3/5

x = 2 and x = -3/5

20.

What do you do to the b value to correctly complete the square?

square it

divide it by 2 and square the result

divide it by 2 and take the square root of the result

divide it by 2 only

21.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

the -4x

the 9

the x²

22.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

Set the equation equal to zero

Divide 10 by 2 and add the result to both sides

Add a² and 10a together

Subtract the 21

23.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

24.

Complete the Square
x² + 6x = 5

(x + 3)² = 5

(x + 6)² = 9

(x + 3)² = 14

(x + 6)² = 14

25.

Complete the square for 2x² - 12x + ____

2x² - 12x + 144

2x² - 12x + 36

2x² - 12x - 36

2x² - 12x + 18

26.

Complete the square for
x² + 12x + ____

x² + 12x + 144

x² + 12x + 36

x² + 12x - 36

x² + +12x - 144

27.

Complete the square for 3x² + 24x + ____

3x² + 24x + 144

3x² + 24x + 36

3x² + 24x + 16

3x² + 24x + 48

28.

Solve by completing the square:

v² + 6v − 59 = 0

{-5 + √50, -5 - √50}

{5 + √50, 5 - √50}

{-3 + √68, -3 - √68}

{3 + √68, 3 - √68}

29.

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

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

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

a = 4, b = 8, c = 3

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

30.

The discriminant is

ax² + bx + c

b - 4ac

b² - 4ac

b² + 4ac

31.

Solve 2x² + 7x - 15 = 0

-1.5 or 5

No Solution

-5 or 1.5

0.7 or 5

100 %

Quadratics Review - Graphing & Solving

Total questions: 31

Worksheet time: 3hrs 41mins

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