Free Printable 8B quadratic functions and equations

Worksheets

8B quadratic functions and equations

Total questions: 25

Worksheet time: 1hrs 9mins

Name

Class

Date

Standard form of a quadratic equation

y=x²

y=ax²+bx+c

y=mx+b

y=x

What is the axis of symmetry formula?

y = (b/2)²

y = ax²+bx+c

b²- 4ac

x = -b/2a

If the graph of a quadratic function bounce at the x-axis at any point, then it has:

1 Real Solution

2 Real Solutions

Half a Solution

No Real Solution

How do you find the vertex?

y = ax² + bx + c

x = -b/(2a) and plug back in for y

x = b/(2a) and plug back in for y

x = -b/a and plug back in for y

x = b/a and plug back in for y

What is the maximum/minimum point of a parabola called?

vertex

intercept

top

bottom

What is another word for zeros?

y-intercepts

roots

vertex

axis of symmetry

Say 'TRUE' or 'FALSE'
Every Quadratic equation has exactly one root

TRUE

FALSE

Which of the following is NOT the method used to solve quadratic equations?

Substitution

Formula

Completing the square

Factorization

The point in which a graph hits the x-axis is know as the _____

Solution

x-intercept

Root

All answers are correct

10.

What are the values of a, b, and c in the quadratic equation 3x² - 10 = -4x

a = 3x² b = -10 c = -4x

a = 3 b = -10 c = -4

a = 3 b = -4 c = -10

a = 3 b = 4 c = -10

11.

How can you tell whether a parabola is facing up or facing down by looking at the equation?

The vertex tells you the direction of the opening

The value of "a" tells you the direction of the opening.

All parabolas open upward

All parabolas open downward

12.

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

Down

Left

Right

13.

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

y = -2

x = 3

x = -3

y = 2

14.

Complete the square for
x² + 12x + ____

x² + 12x + 144

x² + 12x + 36

x² + 12x - 36

x² + +12x - 144

15.

Use the discriminant to find the number of solutions for the following equation.

y = x² +10x + 25

2 solutions

1 solution

0 solutions

16.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

Minimum value, because the a value is positive

Maximum value, because the b value is positive

Maximum value, because the a value is positive

Minimum value, because the c value is negative

17.

What are the solutions for the equation 2x² + 16x = 18

x = -1 and x = 9

x = -9 and x = 1

x = 2 and x= 18

x = 2 and x = 16

18.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

(3,2)

(-3,-2)

(-3,2)

(3,-2)

19.

How many solutions does this graph have?

one

two

no solutions

cannot be determined

20.

$-4x^2-12x+8=0\$
Write the values (separated by commas) that you must substitute in the parenthesis of the formula below with the given quadratic equation $\frac{-\left(\ \right)\pm\sqrt{\left(\ \right)^2-4\left(\ \right)\left(\ \right)}}{2\left(-4\right)}$

(a)

21.

What are the solutions to this equation? (x-3)(x+2)=0

x=3,-2

x=-3,2

x=2,3

x=3,2

22.

√3

±√3

-3

No real solution

23.

The height of a water balloon that is launched into the air is given by h(t) = -16t² + 40t + 12. From what height was the balloon initially launched?

-16 meters

2.8 meters

12 meters

40 meters

24.

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

2.625

6.25

100

210.25

313.5

25.

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. How many seconds is the rocket in the air?

3 sec.

4 sec.

5 sec.

6 sec.

100 %

8B quadratic functions and equations

Total questions: 25

Worksheet time: 1hrs 9mins

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