Free Printable Quadratic Characteristics and Solutions

1.

What is the equation of the axis of symmetry?

a)

y = 4

b)

y = -4

c)

x = 4

d)

x = -4

2.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

3.

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

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

4.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

5.

In the equation y= ax² + bx + c , if a > 0, then...

a)

the graph of the parabola will have a maximum.

b)

the graph of the parabola will open down

c)

the graph of the parabola will open up

d)

the vertex will be (0, 0).

6.

What are the roots of the following quadratic?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

7.

Determine the vertex for the following quadratic: y = x² - 9x + 20

a)

(2,3)

b)

(4,5)

c)

(4.5, -.25)

d)

(-4.5, .25)

8.

Determine if the graph of the parabola

y = −x² + 32x − 41 opens up or down and state whether it is a maximum or minimum point. (select all that apply)

a)

Up

b)

Down

c)

Maximum

d)

Minimum

9.

The graph of a quadratic function is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

10.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

11.

What is the range of this quadratic function?

a)

All real numbers.

b)

y ≥ 4

c)

y < 4

d)

y ≤ 4

12.

What is the domain of this quadratic function?

a)

All real numbers

(- $\infty$ , $\infty$ )

b)

x ≥ 4

c)

x < 2

d)

x ≤ 4

13.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

14.

Determine the interval in which this function is INCREASING.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(∞, -3)

d)

(-∞, -4)

15.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

16.

What is another word for ROOTS?

a)

Zeros

b)

y-intercept

c)

Maximum

d)

Vertex

17.

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

a)

maximum

b)

minimum

18.

Determine the interval of this function's DOMAIN.

a)

(-5, -1)

b)

(-∞, ∞)

c)

No solution

d)

(-∞, -3)

19.

Determine the interval of this function's RANGE.

a)

(-4, ∞)

b)

(-3, ∞)

c)

No solution

d)

(-∞, -4)

20.

Determine the interval in which this function is DECREASING.

a)

(-∞, 2)

b)

(2, ∞)

c)

(2, -∞)

d)

(∞, 2)

21.

Determine the interval of this functions RANGE.

a)

(-∞, 2)

b)

No Solution

c)

(-∞, ∞)

d)

(-∞, 1)

22.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

23.

What direction is the following equation opening?
y=-3x²-7x+8

a)

Up

b)

Down

c)

Left

d)

Right

24.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

25.

What is the range of the function?

a)

y≤3

b)

y≥3

c)

All real numbers

d)

-6≤y≤3

26.

What is the domain of the function?

a)

x≥3

b)

x≤3

c)

All real numbers

d)

-1≤x≤5

27.

On what interval is the function shown increasing?

a)

(-∞, -3)

b)

(-3, ∞)

c)

(-2, ∞)

d)

(-∞, -2)

28.

How many Zeros does this graph have?

a)

one

b)

two

c)

none

d)

cannot be determined

29.

Find the vertex of
f(x) = -x²- 4x + 12

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

30.

When will the graph of y = ax²open downward?

a)

a is a fraction

b)

a is a decimal

c)

a is a negative number

d)

a is a number greater than 1

31.

How many solutions are there?

a)

0

b)

1

c)

2

d)

Cannot be determined

32.

When looking at a quadratic graph, the solution(s) are always the _____________.

a)

y-intercept

b)

vertex

c)

x-intercept(s)

d)

axis of symmetry

33.

What are the solutions when factoring?

a)

x = 6,2

b)

x = -6, -2

c)

x = 8, 12

d)

x = 4, 4

34.

The solution of the quadratic equation
4x²-5x-9=0 are

a)

x=-1 or x=9/4

b)

x=1 or x=9/4

c)

x=2 or x=3

d)

x=-2 or x=-3

35.

The solutions of the quadratic equation
x²-5x+6=0 are

a)

x=1 or x=-6

b)

x=3 or x=2

c)

x=-3 or x= 2

d)

x=-1 or x=6

36.

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.

37.

Find the solutions

x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

38.

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

a)

3

b)

8

c)

-9

d)

-3

39.

Find the solutions.

x²= 18x - 81

a)

x= -9, -9

b)

x= 9, 9

c)

x= -9, 9

40.

Find the solutions.

$5x^2-14x-24$

a)

$x=4\ and\ \frac{6}{5}$

b)

$x=\ 4\ and\ -\frac{6}{5}$

c)

$x=\ -4\ and\ \frac{6}{5}$

d)

$x\ =\ -4\ and\ -\frac{6}{5}$

41.

Solve.

3x² + 5x = 12

a)

x = -4/3, x = 3

b)

x = 4/3, x = -3

c)

x = -1, x = 4

d)

x = 1, x = -4

Quadratic Characteristics and Solutions

Total questions: 41

Worksheet time: 2hrs 46mins

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