Free Printable Quadratic up to Modeling

1.

Tyler wants to know HOW HIGH the soccer ball will get if he kicks it straight up in the air.

When looking at the model on the calculator, which value should we find?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

2.

What is the vertex of the following equation?
y=5(x-3)²+5

a)

(3,5)

b)

(-3,5)

c)

(3, -5)

d)

(-3,-5)

3.

Determine key features from the given function. Choose all that apply

$g\left(x\right)=x^2-6x-7$

a)

Positive function with a minimum

b)

Negative function with a maximum

c)

Vertex located at (3, -16), and an axis of symmetry at x = 3

d)

Vertex located at (3, -16) and an axis of symmetry at y = -16

e)

Reflects over the x-axis

4.

Find how many seconds it takes for the ball to reach its maximum:

y=-16x²+40x+1.5

Hint: Remember -b/2a ?

a)

1.25 sec

b)

1.5 sec

5.

The maximum height of the ball is represented by the...

a)

y-intercept

b)

y coordinate of the vertex

c)

x-intercept

d)

x coordinate of the vertex

6.

Use the graph to determine the solutions.

a)

x=1 and x=5

b)

x=-1 and x=-5

c)

x=-1 and x=5

d)

x=0 and x=5

7.

Convert the following equation from vertex to standard form:

$f\left(x\right)=2\left(x+3\right)^2-2$

a)

$f\left(x\right)=2x^2+16$

b)

$f\left(x\right)=2x^2+8x+14$

c)

$f\left(x\right)=4x^2+24x+36$

d)

$f\left(x\right)=2x^2+12x+16$

8.

Write the equation for the parabola shown in the graph. Write your answer in vertex form.

a)

$y=2\left(x+1\right)^2+8$

b)

$y=-2\left(x+1\right)^2+8$

c)

$y=-\frac{2}{3}\left(x+1\right)^2+8$

d)

$y=\left(x-1\right)^2+8$

9.

A parabola has a vertex at (1,6) and passes through (3,-18). Write the equation in vertex form.

Formula: f(x) = a(x - h)²+ k

a)

f(x) = 3(x - 1)²- 18

b)

f(x) = -6(x - 1)²+ 6

c)

f(x) = 6(x - 3)²- 18

d)

f(x) = -3(x + 1)²- 6

10.

Write the equation for a parabola that has the roots x=2 and x=4 and goes through the point (0, -4).

a)

$y=-\frac{1}{2}\left(x+2\right)\left(x+4\right)$

b)

$y=-\frac{1}{2}\left(x-2\right)\left(x-4\right)$

c)

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

d)

$y=-\frac{1}{2}\left(x-2\right)\left(x-3\right)$

11.

Identify the h and k terms in the following equation: $2\left(x+4\right)^2-1$

a)

h=-4, k=-1

b)

h=4, k=-1

c)

h=4, k=1

d)

h=-4, k=1

12.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

13.

What are the solutions, zeros, or x-intercepts of the graph?

a)

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

b)

(0,0) and (4,0)

c)

(-2,-2)

d)

None

14.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

15.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

16.

What is the y-intercept of the equation
y = 2x²+8x+3?

a)

(0,3)

b)

(3,0)

c)

(0,2)

d)

y=8

17.

A quadratic has two x-intercepts, 1 and 5. It also passes through the point (4, -6). Find the equation of the quadratic.

a)

$2\left(x-1\right)\left(x-5\right)$

b)

$-2\left(x-1\right)\left(x-5\right)$

c)

$\left(\frac{-6}{45}\right)\left(x+1\right)\left(x+5\right)$

d)

$\left(-\frac{6}{45}\right)\left(x+1\right)\left(x+5\right)$

18.

Identify the h and k terms in the following equation: $2\left(x+4\right)^2-1$

a)

h=-4, k=-1

b)

h=4, k=-1

c)

h=4, k=1

d)

h=-4, k=1

19.

Identify the domain and range of the function.

a)

Domain: -6 ≤ x ≤ 2
Range: -3 ≤ y ≤ 5

b)

Domain: All real number
Range: -3 ≤ y ≤ 5

c)

Domain: All real numbers
Range: y ≥ -3

d)

Domain: All real number
Range: y ≤ -3

20.

What is the domain and the range for the graph?

a)

Domain : -2 ≤ x ≤ 2
Range : 0 ≤ y ≤ 4

b)

Domain : 0 ≤ x ≤ 4
Range : -2 ≤ y ≤ 2

c)

Domain : All real #s
Range : y ≤ 4

d)

Domain : -2 ≤ x ≤ 2
Range : y ≤ 4

21.

What is the vertex?
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

22.

Graph the quadratic function

a)

A

b)

B

c)

C

d)

D

23.

Graph the quadratic function

a)

A

b)

B

c)

C

d)

D

24.

Identify the vertex, axis of symmetry, y-intercept, and write the function in vertex form?

$f\left(x\right)=x^2+10x+16$

25.

Write the equation of the quadratic through (2, 5) and x-intercepts of p = 3 and q = -1. Show your work

Quadratic up to Modeling

Total questions: 25

Worksheet time: 1hrs 12mins

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