Free Printable Quadratic practice

1.

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

a)

the -4x

b)

the 9

c)

the x²

2.

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

a)

square it

b)

divide it by 2 and square the result

c)

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

d)

divide it by 2 only

3.

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

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

4.

What does the discriminant determine?

a)

Whether the graph goes up or down

b)

The vertex

c)

The number of Solutions

d)

The y-intercept

5.

What is the discriminant of this graph?

a)

Positive

b)

Zero

c)

Negative

6.

What is the discriminant of this graph?

a)

Positive

b)

Zero

c)

Negative

7.

Find the discriminant: 2a² - 5a + 5 = 0

a)

44

b)

65

c)

-15

d)

-144

8.

Factor and Solve

6x² + 17x + 12 = 0

a)

x = -4/3, x = -3/2

b)

x = 9, x = 8

c)

x = 4, x = 3

d)

x = -4, x = -3

9.

Solve the following by ISOLATION

$4\left(x-5\right)^2=12$

a)

$\left(4x+20\right)^2=12$

b)

$x=5\pm\sqrt[]{3}$

c)

$x=-5\pm\sqrt[]{3}$

d)

$x=5\pm\frac{1}{2}\sqrt[]{3}$

10.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

11.

When using factoring to solve a quadratic equation, what must be true?

a)

The equation must be set equal to 1.

b)

The equation must be set equal to 10.

c)

The equation must be set equal to 0.

d)

It is not necessary to set the equation equal to anything.

12.

What is the color of the graph that has no real zeros?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs have no real zeros

13.

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.

14.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

15.

$3x^2-10x+1=0$

Solve by the method of your choice.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

16.

$7x^2=6x-1$

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)

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

17.

$y\ =\ \left(x-5\right)^2\ +\ 4$ Convert from Vertex to Standard form

a)

$x^2+10x-25$

b)

$x^2-25x+25$

c)

$x^2-25x+4$

d)

$x^2-10x+29$

18.

Which equation shows vertex form of a quadratic function?

a)

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

b)

$f\left(x\right)=ax^2+bx+c$

c)

$f\left(x\right)=a\left(x-r_1\right)\left(x-r_2\right)$

d)

$x=-\frac{b}{2a}$

19.

Convert to vertex form.

a)

y=-(x-5)² + 21

b)

y=-(x+5)² + 21

c)

y=-(x+10)² + 21

d)

y=-(x-10)² + 21

20.

Convert f(x) = 3x²+ 6x - 5 to vertex form.

a)

f(x) = 3(x + 1)² - 8

b)

f(x) = 3(x - 1)² - 8

c)

f(x) = 3(x + 2)² - 8

d)

f(x) = 3(x - 2)² - 8

21.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

22.

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

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

23.

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

24.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

25.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

f(x) = (x - 4)² + 65

26.

Convert f(x) = 4x² - 32x + 2 to vertex form.

a)

f(x) = 4(x + 4)² - 62

b)

f(x) = 4(x - 4)² - 62

c)

f(x) = 4(x - 8)² - 62

d)

f(x) = 4(x + 8)² - 62

27.

The pathway of an arrow can be represented by the equation h = -16t² + 80t + 25, where h is the height in feet and t is the time in seconds. What is the maximum height?

a)

h = 125 feet

b)

h = 80 feet

c)

h = 95 feet

d)

h = 140 feet

28.

A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take the rock to reach the river (ground)?

a)

4.5 seconds

b)

2.5 seconds

c)

3.8 seconds

d)

3.5 seconds

29.

Joe Mauer hits a fly ball. You can track the height of the ball using the equation: h(t) = -16t² + 140t + 2. What is the starting height of the ball?

a)

-16 feet

b)

140 feet

c)

2 feet

d)

0 feet

30.

A baseball was thrown from a height of 5 feet with an initial velocity of 24 feet per second at an angle above the horizontal. Write an equation to represent the situation.

a)

y= -16x²+ 24x + 5

b)

y= -16x²+ 24x - 5

c)

y= 16x²+ 24x + 5

d)

y= x²+ 24x + 5

31.

Charlie shoots a basketball from a height of 6 feet with an initial upward velocity of 18 feet per second. How long will it take the ball to reach the maximum height?

a)

0.6 seconds

b)

11 seconds

c)

6 second

d)

this graph has a minimum

32.

The height of an object thrown into the air can be modeled by the formula $y=-16x^2+70x+95$ , where y is in feet after x seconds.
What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

33.

A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
$h=-16t^2+64t+960$
How many seconds did it take for the ball to reach its maximum height?

a)

10 seconds

b)

64 seconds

c)

960 seconds

d)

2 seconds

34.

A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
$h=-16t^2+64t+960$
What is the maximum height reached?

a)

1024 feet

b)

64 feet

c)

960 feet

d)

2 feet

35.

A ball is hit into the air with an initial velocity of 100 ft/s. Its height, h, after t seconds is given by the function

h = -16t² + 100t + 5

How many seconds did it take for the ball to reach its maximum height?

a)

3.654 seconds

b)

2.451 seconds

c)

161.25 seconds

d)

3.125 seconds

Quadratic practice

Total questions: 35

Worksheet time: 3hrs 50mins

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