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Key Features of Quadratics

Total questions: 57

Worksheet time: 1hrs 23mins

Name
Class
Date
1.

Quadratic equations take the shape of a _______ when graphed.

a)

parabola

b)

straight line

c)

snaked line

d)

elliptical

2.
The highest or lowest point on a quadratic is called the...
a)
Max
b)
Vertex
c)
Axis of Symmetry
d)
Intercept
3.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

4.
Standard form of a quadratic equation
a)
y=x²
b)
y=ax²+bx+c
c)
y=mx+b
d)
y=x
5.
Which of the following equations matches vertex form of a quadratic?
a)
ax + by = c
b)
y = a(x - h)2 + k
c)
y = ax2 + bx + c
d)
y = mx + b
6.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

y intercept

7.

Which of the following are all the different ways to name the solutions to a quadratic equation?

(Choose all that apply)

a)

Vertex

b)

Root

c)

Zero

d)

Quartic

e)

x - intercept

8.

Does this graph have a maximum or a minimum?

a)

maximum

b)

minimum

c)

I am not sure.

d)

neither

9.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

10.

Use the picture to find the vertex and axis of symmetry:

a)

Vertex (3,8) Axis x = 3

b)

Vertex (3,8) Axis y = 3

c)

Vertex (8,3) Axis x = 3

d)

Vertex (8,3) Axis y = 3

11.

Determine the domain and range of the function

a)

Domain: All real numbers

Range: All real numbers

b)

Domain: x ≥ -4

Range: All real numbers

c)

Domain: All real numbers

Range: y ≥ -4

d)

Domain: -1 ≤ x ≤ 5

Range: y ≥ -4

12.

Does y = -4x2 have a maximum or minimum value?

a)
maximum
b)
minimum
13.

Identify the 'a' value of the quadratic equation:

y = 16x2 - 8x - 24

a)

16

b)

8

c)

-8

14.

Identify the 'b' value of quadratic equation written in standard form?

y = 16x2 -8x - 24

a)

16

b)

-8

c)

8

15.

Which value is the vertex?

a)

(-4, 0)

b)

(-1, -9)

c)

(0, -8)

d)

(2, 0)

16.

Use the graph to determine the X-intercepts:

a)

(-1,0) and (-3,0)

b)

(1,0) and (3,0)

c)

(0,1) and (0,3)

d)

(0,-1) and (0,-3)

17.

What is the equation for the axis of symmetry?

a)

x = 2

b)

x = 6

c)

x = 3

d)

x = 0

18.

What is the vertex of this quadratic equation?

y=2(x−3)2+6y=2\left(x-3\right)^2+6  

a)

(2, 6)

b)

(3, 6)

c)

(2, -3)

d)

(-3, 6)

19.

What is the vertex of the quadratic function:

f(x) = x2 - 6x + 11

Hint: Use Desmos

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

20.

If the blue graph is f(x) = x2

then the red must be...

a)

g(x) = x2 - 5

b)

g(x) = x2 + 5

c)

g(x) = (x - 5)2

d)

g(x) = (x + 5)2

21.

What are the x-intercepts?

a)

(0,0) and (2,0)

b)

(-4,0) and (0,0)

c)

(0,0) and (0,4)

d)

(0,0) and (4,0)

22.

What is the significance of the ordered pair (0, -2) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

23.

What is the equation of the axis of symmetry?

a)

y = 0

b)

x = 0

c)

x = 3

d)

x = -3

24.
What is the vertex of the graph?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
25.
.How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
26.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
all real numbers
27.

When did the ball reach its maximum height? Choose the key feature and the answer.

a)

y-intercept, 3 secs

b)

x-value of the vertex, 4 secs

c)

y-value of the vertex, 5 secs

d)

y-intercept, 0 secs

28.

What was the maximum height of the ball? Choose the key feature and the answer choice.

a)

y-intercept, 3 feet

b)

y-intercept, 0 feet

c)

x-value of the vertex, 4 feet

d)

y-value of the vertex, 5 feet

29.

How high was the ball when it was thrown? Choose the key feature and the answer.

a)

y-intercept, 0 feet

b)

y-intercept, 3 feet

c)

x-value of the vertex, 4

d)

y-value of the vertex 5

30.

What was the height of the ball at 1 second?

a)

3 feet

b)

4 feet

c)

5 feet

31.

When did the water reach its maximum height? Choose the key feature and the answer.

a)

x-value of vertex, 2 seconds

b)

y-value of vertex, 9 seconds

c)

y-intercept, 0 seconds

d)

x-intercept, 3.8 seconds

32.

What was the maximum height of the water? Choose the key feature and the answer.

a)

y-intercept, 0 feet

b)

x-value of the vertex, 2 feet

c)

y-value of the vertex 10 feet

d)

x-intercept. 3.85 feet

33.

What was the height of the water at 3 seconds?

a)

9 feet

b)

10 feet

c)

7 feet

d)

5 feet

34.

Approximately how long did it take the water from the fountain to hit the pool below?

a)

about 1.85 second

b)

about 2.85 seconds

c)

about 3.85 seconds

d)

about 4.85 seconds

35.

Approximately when did the ball hit the ground?

a)

3.25 seconds

b)

4.25 seconds

c)

8.25 seconds

d)

10.25 seconds

36.

What key feature tells the initial height of the roller coaster?

a)

y-intercept

b)

x-intercept

c)

axis of symmetry

d)

vertex

37.

What was the approximate initial height of the roller coaster?

a)

150

b)

120

c)

100

d)

50

38.

What key feature tells the lowest point on the roller coaster?

a)

y-intercept

b)

vertex

c)

Axis of Symmetry

d)

x-intercept

39.

What is the approximate lowest height of the roller coaster?

a)

120 feet

b)

3 feet

c)

25 feet

d)

170 feet

40.

What was the height of the roller coaster at 6 seconds?

a)

120 feet

b)

50 feet

c)

25 feet

d)

100 feet

41.

What is the sign of the "a" value for this graph?

a)

positive

b)

Negative

42.

What is the sign of the "a" value for this graph

a)

negative

b)

positive

43.

Does this scenario have a max or a min?

a)

Max

b)

Min

44.

What is the equation for the axis of symmetry?

a)

x = b / 2

b)

x = 2a / -b

c)

x = 2 / b

d)

x = -b / 2a

45.

How do I find the y-value of the vertex?

a)

factor

b)

x = -b / 2a gives you the y-value of the vertex

c)

find x = -b / 2a and then plug in for x and solve for y.

d)

find -b / 2a and then plug in for y and solve for x.

46.

Which of the following are examples of quadratic equations?

a)

2x+3

b)

2x2+2

c)

x-4x2

d)

x3

e)

x2

47.

The graph of a Quadratic function is shown. Select ALL the statements that are true about the graph.

a)

It has a Maximum

b)

The Zeros/Solutions are 0 and 4

c)

It has a Minimum

d)

The Vertex is (0, 0)

e)

The Axis of Symmetry (AOS) is x = 2

48.

The graph of a Quadratic function is shown. Select ALL the statements that are true about the graph.

a)

it has a minimum

b)

it has a maximum

c)

the x - intercepts are (1, 0) and (3, 0)

d)

The y - intercept is (0, 0)

e)

The axis of symmetry is x = 2

49.

The graph of a Quadratic function is shown. Select ALL the statements that are true about the graph.

a)

it has minimum

b)

it has a maximum

c)

The y - intercept is (0, 0)

d)

There is only one x-intercept

e)

In the equation ax2 + bx + c, the value of "a" would be negative x because the Parabola opens down.

50.
Which of the following is the vertex of the graph?
a)
(2, 0)
b)
(-2, 0)
c)
(0, 4)
d)
(-1, 3)
51.

The set of all y values used in a function's graph is called what?

a)

Increasing interval

b)

Decreasing interval

c)

Domain

d)

Range

52.

The set of x values for which the graph goes upward is called what?

a)

Increasing interval

b)

Decreasing interval

c)

Domain

d)

Range

53.
What is the range of this function?
a)
(- ∞,+∞)
b)
[0, +∞)
c)
[-2, +∞)
d)
[2, +∞)
54.
What's the y-intercept of y = 3x2- 6x + 4
a)
(4,0)
b)
(-4,0)
c)
(0,-4)
d)
(0,4)
55.

Which function has a smaller y-intercept?

a)

y=(x+1)(x+2)y=\left(x+1\right)\left(x+2\right)

b)

y=3(x+1)2+7y=3\left(x+1\right)^2+7

56.

Compare the function below to the graph pictured. Which has a larger maximum?

f(x)=−x2+6x−2f\left(x\right)=-x^2+6x-2  

a)

Graph

b)

Equation

57.

Compare the function below to the graph pictured. Which has a lower minimum?

f(x)=x2+6x+20f\left(x\right)=x^2+6x+20  

a)

Graph

b)

Equation

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