Free Printable Quiz 3.2 Quadratic Equations and Solving by Extracting Roots

1.

Determine the roots of the quadratic equation $x^2 - 9 = 0$ .

a)

$x = 3, x = -3$

b)

$x = 9, x = -9$

c)

$x = 0, x = 9$

d)

$x = 0, x = -9$

2.

Anika, Elijah, and Benjamin are trying to find the vertex of a parabolic path of a ball thrown in the air. The path of the ball is represented by the equation $\frac{1}{2}\left(x+4\right)^2+1$ . Can you help them determine the vertex of this path?

(a)

3.

Aiden, Michael, and Rohan are trying to launch a rocket. They notice that the rocket's flight path forms a parabola. What TWO solutions represent the way they could write the RANGE of this parabola?

a)

A

b)

B

c)

C

d)

D

4.

Avery, Evelyn, and Samuel are studying the properties of parabolas. They are trying to identify the vertex of a particular parabola. Can you help them determine the vertex?

(a)

5.

Ava, Aiden, and Maya are studying the graph of a quadratic function. They are trying to understand the vertex form of a quadratic function. What does the k term tell them?

a)

It tells them the direction of the graph is up.

b)

It tells them the direction of the graph is down.

c)

It tells them whether the graph goes up or down, and the y-value in the vertex.

d)

It doesn't tell them anything.

6.

Harper is studying quadratic equations in her math class. She comes across the equation $2\left(x+4\right)^2-1$ in her textbook. Can you help her identify the a, h, and k terms in this equation?

a)

a=2, h=-4, k=-1

b)

a=-2, h=4, k=1

c)

a=2, h=4, k=1

d)

a=-2, h=-4, k=1

7.

Evelyn, Aiden, and Abigail are trying to solve a real-world problem using a quadratic equation. They came up with the equation
4x² – 8x = 3. Can you help them determine the values of
a, b, and c in their equation?

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

8.

Charlotte is studying the trajectory of a ball thrown in the air. She models the trajectory with the equation y = -(x - 4)² - 3. Aiden asks her, does this trajectory have a maximum or minimum height?

a)

Maximum

b)

Minimum

9.

Arjun is studying the path of a ball thrown in the air. The line of symmetry of the ball's path passes through which point?

a)

The point where the ball was initially thrown

b)

Any random point in the path

c)

The highest point the ball reaches

d)

A point symmetrical to the highest point the ball reaches

10.

Benjamin, Liam, and Samuel are studying graphs in their math class. They come across a graph with a green dashed line. What is this green dashed line called in their study material?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

11.

Abigail is studying the graph of a quadratic function in her math class. She learns that this graph is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

12.

How can the graph of $f\left(x\right)=\left(x-2\right)^2-5$ , 5 be obtained from the graph of $y=x^2$

a)

Shift the graph 2 units left and 5 units down.

b)

Shift the graph 5 units right and 2 units down.

c)

Shift the graph 2 units left and 5 units up.

d)

Shift the graph 2 units right and 5 units down.

13.

Which of the following square root is NOT a perfect square root ?

a)

$\sqrt{45}$

b)

$-\sqrt{400}$

c)

$\sqrt{0.09}$

d)

$\sqrt{\frac{9}{49}}$

14.

What are the roots / solutions of the quadratic equation equation 2x² + 3 = 101 ?

a)

x = + 7

b)

x = + 8

c)

x = + 9

d)

x = + 10

15.

1What are the roots / solutions of the quadratic equation (x+ 1)² = 50?

a)

$x\ =\ -1\pm2\sqrt{25}$

b)

$x\ =\ 1\pm2\sqrt{25}$

c)

$x\ =1\pm\ 5\sqrt{2}$

d)

$x\ =\ -1\pm5\sqrt{2}$

16.

Find the solution(s) of the given quadratic equation $\left(x+3\right)^2=100$

a)

$x=\pm10$

b)

$x=7\ \ \ or\ \ \ \ x\ =13$

c)

$x=7\ \ \ \ or\ \ \ \ x\ =-13$

d)

$x=\pm7$

17.

Which of the following is a quadratic equation?

a)

$x\left(x+3\right)=0$

b)

$4\left(x-2\right)=0$

c)

$x\left(x-7\right)^2=0$

d)

$x+8=3x-9$

18.

Solve by extracting square roots:

(x - 2 )² = 49

a)

x = 5 and x = -9

b)

^{x = 7 and x = -7}

c)

x = 9 and x = -5

d)

^{x = 9 and x = -9}

19.

Solve by extracting square roots:

5(x - 3)² + 1 = 81

a)

x = -1, 7

b)

x = -7, 1

c)

x = ± 9

d)

x = 3, 10

20.

What appropriate method of solving can we used in the equations that are written in the form x² = c?

a)

factoring

b)

quadratic formula

c)

extracting square roots

d)

completing the square

21.

Which of the following has a solution of x = 5?

a)

x² – 5 = 0

b)

x² – 50 = 0

c)

2x² – 50 = 0

d)

2x² – 10 = 0

22.

What are the roots of the quadratic equation (s - 4)² - 81 = 0?

a)

s = 9/2 and s = -9/2

b)

s = 9 and s= -9

c)

s = 2 and s = -2

d)

s = 13 and s = -13

23.

John is solving for equation (3y – 3)² – 144 = 0 by extracting square roots. Which of the following solution will arrive?

a)

5 and –3

b)

–5 and 3

c)

7 and –4

d)

–12 and 3

24.

Solve.

x²- 4 = 76

a)

No Real Number Solution

b)

x = ±4√5

c)

x = ±80

d)

x = ±5√4

25.

Write the expression in simplest radical form.

$\sqrt[]{245}$

26.

Simplify $\sqrt[]{32}$

a)

$\sqrt[]{32}$

b)

$16\sqrt[]{2}$

c)

$4\sqrt[]{2}$

d)

$2\sqrt[]{8}$

27.

What piece of information does c identify in the following equation?
y=ax²+bx+c

a)

Zeroes

b)

Axis of Symmetry

c)

Direction

d)

y-intercept

28.

What are the x-intercepts?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

29.

Identify the x-intercepts:

y= -3(x-5)(x+5)

a)

(-3,0) and (5,0)

b)

(5,0) and (-5,0)

c)

(5,0) and (0,5)

d)

(0,5) and (0,-5)

30.

What relationship does the vertex of a parabola always have with the x-intercepts?!

a)

It's the same as one of the numbers

b)

It's the average of the zeros

c)

It's the same as the y-intercept

d)

It's the maximum

31.

What is the equation for this parabola in factored form?

a)

y=(x+2)(x-1)

b)

y=(x-2)(x+1)

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

32.

What are the x-intercepts of the parabola?
y = ¼(x + 2)(x - 6)

a)

-2 and 6

b)

2 and -6

c)

-2

d)

¼ and -2 and 6

33.

If the vertex is (9,17), the axis of symmetry is ___.

a)

x = 9

b)

x = 17

34.

Identify the vertex

a)

(-1,-9)

b)

(0,-8)

c)

(-4,0)

d)

(0,0)

35.

If the vertex of a parabola is $\left(6,-6\right)$ The Axis of Symmetry uses the h portion of the vertex. Then the range will use the (a) part of the vertex's ordered pair. The range of a parabola uses the greater than or equal to (b) if the vertex is a minimum, and uses the less than or equal to (c) symbols if the vertex is a maximum. This vertex is a (d) so the answer would be (e) .

Choose from the below words

$\left(y\ge k\right)$

$\left(y\le k\right)$

k

$\left(y\ge-6\right)$

\left(y\le6\right)

minimum

maximum

36.

A quadratic function in vertex form is given as $f(x)=−2(x+4)^2+7$ . What are the coordinates of the axis of symmetry and the maximum value of the function?

a)

Axis of symmetry: x=4, Maximum value: y=7

b)

Axis of symmtry: x = -4 , Maximum value: y = -2

c)

Axis of symmetry: x = -4, maximum value: y=7

d)

Axis of symmetry: x = 4, maximum value: y = -7

37.

Which of the following best explains why the vertex form of a quadratic equation is useful?

a)

It directly provides the x-intercepts.

b)

It allows for easy determination of the vertex and axis of symmetry.

c)

It simplifies factoring the quadratic equation.

d)

It eliminates the need to use the quadratic formula.

38.

A toy rocket follows the trajectory given by $h(x)=−3x^2+18x$ , where h(x) is the height in meters.

How far horizontally from the launch point does the rocket reach its highest point?

a)

x =3

b)

x = 6

c)

x = 9

d)

x = 18

Quiz 3.2 Quadratic Equations and Solving by Extracting Roots

Total questions: 38

Worksheet time: 2hrs 7mins

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