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9-1 Solving Quadratic Functions

Total questions: 50

Worksheet time: 13hrs 30mins

Name
Class
Date
1.
Find the zeros.
a)
0 and 4
b)
0 and -4
c)
0
d)
-4
2.
True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing.
a)
True
b)
False, because the solution and root are the same but the x-intercept and zero are different
c)
False, because the x-intercept and root are the same but the zero and solution are different
d)
False, they are all different
3.

Graph the quadratic function on your calculator.

Find the zeros.

5x2 - 35x + 60 = 0

a)

x = 3,  -4

b)

x = -3,  4

c)

x = 3,  4

d)

x = -3,  -4

4.

Graph the quadratic function on your calculator.

Find the zeros.

4x2+2x - 6 = 0

a)

x = 1 & -1.5

b)

x = -1 & 1.5

c)

x = 1

d)

x = -1.5

5.

Graph the quadratic function on your calculator.

Find the zeros.

x2+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

d)

No solution

6.

Graph the quadratic function on your calculator.

Find the zeros.

x2-14x-51=0

a)

x= 17, -3

b)

x= -17, 3

c)

x= -17, -3

d)

x = -3

7.

Graph the quadratic function on your calculator.

Find the zeros.

x2 - 5x = 14

a)

x= -7, -2

b)

x= 7, -2

c)

x= -7, 2

d)

No Solution

8.

Graph the quadratic function on your calculator.

Find the zeros.

3x2 + 9x = 30

a)

x= 2, -5

b)

x= 5, -2

c)

x= -5, -2

d)

x = 2, 5

9.

Graph the quadratic function on your calculator.

Find the zeros.

x2 - 6x + 8 = 0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

10.

Graph the quadratic function in your calculator.

Find the roots.

y=x2−3x+2y=x^2-3x+2  

a)

-1 and -2

b)

No Solution

c)

2

d)

1 and 2

11.

Graph the quadratic function in your calculator.

Then, find the zeros.

−x2−7x=6-x^2-7x=6  

a)

x=1 and x=6x=1\ and\ x=6  

b)

x=−6x=-6  

c)

x=−6 and x=−1x=-6\ and\ x=-1  

d)

No Solutions

12.

Graph the quadratic function using your calculator. Find the solutions.

y=−0.5x2−x−6y=-0.5x^2-x-6  

a)

-2 and 4

b)

No Solution

c)

-6

d)

-1 and 1.2

13.

Determine how many solutions:

a)

One Solution

b)

Two Solutions

c)

No Solutions

d)

Infinitely Many Solutions

14.

Determine how many roots:

a)

One Solution

b)

Two Solutions

c)

No Solutions

d)

Infinitely Many Solutions

15.
What are the values of x when y = 0?
a)
{ -3, 1 }
b)
{ -2 }
c)
{ -3, -1 }
d)
{ 1, 3 }
16.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
17.
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
18.

ax2 + bx + c = 0  is the standard form of a quadratic equation.

a)

True

b)

False

19.

Graph the quadratic function.

Which is the correct graph of the function?

a)
b)
c)
d)
20.

According to the graph, where are the solutions to the equation below?

0 = -x2 - 2x + 3

a)

x = 2

b)

x = -3, x = 1

c)

x = 3, x = 0

d)

No Solutions

21.

Determine how many roots:

a)

One Solution

b)

Two Solutions

c)

No Solutions

d)

Infinitely Many Solutions

22.

To solve a quadratic by graphing is to find where the parabola crosses the x-axis. We call these the ___. Select all that apply.

a)

zeroes

b)

x-intercepts

c)

solutions

d)

roots

e)

y-intercepts

23.

Graph the quadratic function using your calculator.

Find the zeros.

2x2+7x=152x^2+7x=15  

a)

x = -1.5 and  x = 5

b)

No Solutions

c)

x = -5 and x = 1.5

d)

x = 0.7 and x = 5

e)

x = -1.5 only

24.

We can see the y-intercept when a quadratic function is written in...

a)

Vertex Form

b)

Standard Form

c)

Factored Form

25.

What is the y-intercept of the quadratic function?

y = x2 - 6x + 5

a)

(0, 8)

b)

(0, - 6)

c)

(5, 0)

d)

(0, 5)

26.

What is the y-intercept of the quadratic function?

y = 2x2 - 2x + 1

a)

(1,0)

b)

(-2,0)

c)

(0,1)

d)

(0, -1)

27.

Graph on your calculator. Does this equation open up or down? 

y = -3x2 +7x - 2

a)

up

b)

down

c)

Neither; it opens to the right.

d)

Neither; it opens to the left.

28.
What is the maximum/minimum of a parabola called?
a)
vertex
b)
point
c)
top
d)
bottom
29.
Where is the axis of symmetry for this parabola?
a)
x = −1
b)
x = 0
c)
y = 3
d)
x = −3
30.
What is the formula above primarily used for?
a)
Finding the axis of symmetry from standard form
b)
Finding the vertex from standard form
c)
Finding the vertex from vertex form
d)
Finding the vertex from standard form
31.
What are the zeros of the parabola? 
a)
1, 5
b)
3, -5 
c)
3, 0
d)
-6, 1
32.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
33.
Which of the following functions graphs the parabola shown?
a)
y = -x2 - 6
b)
y = -x2 + 6
c)
y = x2 - 6
d)
y = x2 + 6x
34.
Which of the following functions graphs the parabola shown?
a)

y = x2 - 4x + 4

b)

y = -2x2 - 8x - 3

c)

y = x2 - 4x + 5

d)

y = 2x2 - 6x + 1

35.
Which of the following functions graphs the parabola shown?
a)

y = x2 - 4x + 1

b)

y = -2x2 - 8x - 3

c)

y = x2 - 4x + 5

d)

y = 2x2 + 6x + 1

36.

How may one graph a function in the TI-84 calculator?

a)

Type the function appropriately in "y=", then press "graph".

b)

Using the home screen, enter the function, then press "enter".

c)

Go to "STAT" mode, enter the function appropriately, then press "enter".

37.

How may someone correctly generate a table of values using the TI-84?

a)

Enter the function appropriately in "y=", press "2nd", then press "graph".

b)

Press "PRGM", then following the prompts.

c)

Press "ALPHA" to set up columns, then press "table".

d)

Go to "STAT" mode to activate the appropriate columns.

38.

When using "y=", which of the following is true?

a)

Only numbers are allowed as entries.

b)

All variables are permitted.

c)

If a variable is needed, only use "X" as a designated variable.

d)

Multiple rows are not allowed.

39.

In order to activate a function or character that is shown in blue on the calculator panel, which of the following options must one press first?

a)

"2nd" .

b)

"ALPHA"

c)

"APPS"

d)

"STAT"

40.

In order to activate a function or character that is shown in green on the calculator panel, which of the following options must one press first?

a)

"STAT"

b)

"ALPHA"

c)

"y="

d)

"2nd"

41.

Can you use a TI-84 calculator during tests, quizzes, and EVEN ON THE STATE TEST this school year?

a)

Yes

b)

No

c)

I am not sure.

42.

What key on the calculator represents the "equal" sign?

a)

2nd blue key

b)

alpha green key

c)

enter key

d)

I don't know

43.

What key on the calculator represents the "negative" sign?

a)

the minus sign

b)

(-)

c)

The N key

d)

The Enter key

44.

What key on the calculator do you use to enter the variable "x"?

a)

The apps key

b)

The 2nd key

c)

I don't know

d)

The key next to the alpha key

45.

What happens if I press "2nd, mode" on the calculator?

a)

The calculator quits whatever it is doing

b)

The calculator erases everything

c)

The calculator speeds up whatever it is doing

d)

The calculator will change everything to a fraction

46.

True or False: On the calculator, you may use the subtract button as the negative sign.

a)

True

b)

False

47.

When finding the x-intercepts using the TI-84 graphing calculator, which option do you choose from the CALCULATE menu?

a)

1: value

b)

2: zero

c)

3: minimum

d)

4: maximum

48.

What key on the calculator can you use to square a number?

a)

The alpha key

b)

The math key

c)

The ∧\wedge  key

d)

The x "squared" key

49.

What is vertex form of a quadratic function?

a)
ax2 + bx + c
b)
a(x - h)2 + k
c)
y - y1 = m(x - x1)
d)
Ax + By = C
50.

What is standard form of a quadratic function?

a)
ax2 + bx + c
b)
a(x - h)2 + k
c)
y - y1 = m(x - x1)
d)
Ax + By = C

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