Free Printable Unit 6 Test Review

1.

The U-Shaped curve of a quadratic equations is called a ______

a)

parabola

b)

maximum

c)

minimum

d)

bolapara

2.

Standard Form of a Quadratic Equation :

a)

y = ax + B + C

b)

y= ax² + bx + C

c)

a + b + c = 0

3.

What is the vertical line that divides the parabola into two equal parts?

a)

parabola

b)

vertex

c)

axis of symmetry

d)

unicorns

4.

The axis of symmetry passes through which coordinate?

a)

y coordinate of the vertex

b)

x coordinate of the vertex

c)

always goes through the origin

d)

always goes through the x-intecept

5.

A vertex that represents the LOWEST point on a graph is called _____

a)

maximum

b)

minimum

c)

vertex

d)

home run

6.

When the vertex is the highest point it is called ____

a)

tipping point

b)

maximus prime

c)

minimum

d)

maximum

7.

A vertex can be defined as _______

a)

the turning point of the parabola

b)

the maximum

c)

the minimum

d)

all of the above

8.

The formula to find the Axis of Symmetry :

a)

b)

c)

9.

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

a)

y = -2

b)

x = 2

c)

x = -3

d)

y = -3

10.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

11.

Which equation is Vertex Form?

a)

y=ax²+bx+c

b)

y=a(x-h)²+k

12.

What is the domain of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ 0

d)

x ≥ 0

13.

What is the range of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ 0

d)

x ≥ 0

14.

What is the domain of the graph?

a)

$\left(-\infty,\ \infty\right)$

b)

To infinity and beyond

c)

$\left[-\infty,\ \infty\right]$

d)

$\left[0,\ \infty\right)$

15.

What is the range of the graph?

a)

$\left[0,\ \infty\right)$

b)

$\left(-1,\ \infty\right)$

c)

$\left[-1,\ \infty\right)$

d)

$\left(0,\ \infty\right)$

16.

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

17.

Name the indicated parts of the equation

y=\left(x+4\right)^2-1

a)

Vertex: (-1, -4); minimum; opens up
A.O.S.: x = -1
y intercept: (0,15)

b)

Vertex: (-1, -4); maximum; opens down
A.O.S.: x = -1
y intercept: (0,15

c)

Vertex: (-4, -1); minimum; opens up
A.O.S.: x = -4
y intercept: (0,15)

d)

Vertex: (-4, -1); maximum; opens down
A.O.S.: x = -4
y intercept: (0,15)

18.

Name the indicated parts of the equation

y=x^2-4x

a)

x intercepts: (0, 0) and (4, 0)
Vertex: (2, -4); opens up; minimum
y intercept: (0,0)
Vertex form: $y=\left(x-2\right)^2-4$

b)

x intercepts: (2, 0) and (-4, 0)
Vertex: (2, -4); opens up; minimum
y intercept: (0,0)
Vertex form: $y=\left(x-2\right)^2-4$

c)

x intercepts: (2, 0) and (-4, 0)
Vertex: (2, -4); opens up; minimum
y intercept: (0,0)
Vertex form: $y=\left(x-4\right)^2-2$

d)

x intercepts: (0, 0) and (4, 0)
Vertex: (2, -4); opens up; minimum
y intercept: (0,0)
Vertex form: $y=\left(x-4\right)^2-2$

19.

What is the domain of the graph?

a)

[1,∞)

b)

(-∞,1]

c)

(-∞,∞)

d)

[-∞,∞]

20.

Write the interval notation as an inequality. (-∞, 5]

a)

x > 5

b)

x ≥ 5

c)

x < 5

d)

x ≤ 5

21.

In interval notation, positive and negative ∞ are always closed in by ______.

a)

( ) Parentheses

b)

[ ] Square Brackets

c)

{ } Curly Brackets

22.

DOMAIN is found by reading the ends of a graph from ___ to ___.

a)

Right to left

b)

Left to right

c)

Bottom to top

d)

Top to bottom

23.

RANGE is found by reading the ends of a graph from ___ to ___.

a)

Right to left

b)

Left to right

c)

Bottom to top

d)

Top to bottom

24.

Write the following range in set builder notation:

(4, ∞).

a)

{y | y > 4}

b)

{y | y > 4}

c)

{x | x < 4}

d)

{x | x > 4}

25.

Given {x| x ≥ 6}, the domain of a function in set builder notation, which of the following rewrites it in interval notation?

a)

$\left(6,\ \infty\right)$

b)

$\left[6,\infty\right)$

c)

$\left(-\infty,6\right)$

d)

$\left(-\infty,6\right]$

26.

Name the indicated parts of the equation.

y=x^2-8x+18

a)

Vertex: (4,2); opens up; minimum
A.O.S.: x = 4
y intercept: (0,18)
Vertex form: $y=\left(x-4\right)^2+2$

Domain:

\left(-\infty,\ \infty\right)

Range:

\left[2,\ \infty\right)

b)

Vertex: (4,2); opens up; minimum
A.O.S.: x = 4
y intercept: (0,18)
Vertex form: $y=\left(x-4\right)^2+2$
Domain: $\left(-\infty,\ \infty\right)$ Range: $\left[-4,\infty\right)$

c)

Vertex: (4,2); opens up; minimumA.O.S.: x = 4y intercept: (0,18)Vertex form: $y=\left(x+2\right)^2-4$
Domain: $\left(-\infty,\ \infty\right)$ Range: $\left[2,\ \infty\right)$

d)

Vertex: (4,2); opens up; minimum
A.O.S.: x = 4
y intercept: (0,18)
Vertex form: $y=\left(x+2\right)^2-4$
Domain: $\left(-\infty,\ \infty\right)$ Range: $\left[-4,\infty\right)$

27.

Name the indicated parts of the equation

y=-2\left(x-6\right)\left(x+2\right)

a)

x intercepts: (-2, 0) (6, 0)
Vertex: (-2, 6); opens down; maximum
y intercept: (0, 24)
multiply the y values by: -2
Vertex Form: $y=-2\left(x+2\right)^2+6$

b)

x intercepts: (-2, 0) (6, 0)
Vertex: (-2, 6); opens down; maximum
y intercept: (0, 24)
multiply the y values by: -2
Vertex Form: $y=-2\left(x-2\right)^2+6$

c)

x intercepts: (-2, 0) (6, 0)
Vertex: (2, 32); opens down; maximum
y intercept: (0, 24)
multiply the y values by: -2
Vertex Form: $y=-2\left(x+2\right)^2+32$

d)

x intercepts: (-2, 0) (6, 0)
Vertex: (2, 32); opens down; maximum
y intercept: (0, 24)
multiply the y values by: -2
Vertex Form: $y=-2\left(x-2\right)^2+32$

28.

A quadratic function has the given roots. Write an equation for the quadratic in standard form, $y=ax^2+bx+c$ Start by setting the roots equal to x

Roots: 3 and -5

a)

$y=x^2-2x-15$

b)

$y=x^2+2x-15$

c)

$y=x^2+2x+15$

d)

$y=x^2-2x+15$

29.

$y=ax^2+bx+c$

A quadratic function has the given roots. Write an equation for the quadratic in standard form. Start by setting the roots equal to x

Roots: $\pm3i$

a)

$y=x^2-9$

b)

$y=x^2+9$

c)

$y=\left(x+3\right)\left(x-3\right)$

d)

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

30.

Write a quadratic function in the given form for a graph with the characteristics:

Vertex: (2, 5)

passes through: (3, 7)

a)

$y=2\left(x-2\right)^2+5$

b)

$y=3\left(x-2\right)^2+5$

c)

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

d)

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

31.

Write a quadratic function in the given form for a graph with the characteristics:

x intercepts: -4, 2

passes through: (4, 8)

a)

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

b)

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

c)

$y=8\left(x+4\right)\left(x-2\right)$

d)

$y=8\left(x-4\right)\left(x+2\right)$

32.

$y=5\left(x+4\right)^2+3$

Rewrite the equation in standard form

a)

$y=5x^2+40x+83$

b)

$y=5x^2+20x+15$

c)

$y=5x^2+4x+15$

d)

$y=5x^2+20x+3$

33.

$y=-3\left(x-4\right)\left(x+5\right)$

Rewrite the equation in standard form:

a)

$y=-3x^2-3x+60$

b)

$y=-3x^2-x-20$

c)

$y=-5x^2-11x+60$

d)

$y=-5x^2-11x+20$

34.

Draw a picture, write the equation and solve.

The length of a rectangle is 4 feet less than four times the width. The area of the recentangle is 120 ft². What are the dimensions of the rectangle in feet?

a)

width: 30 feet

length: 4 feet

b)

width: 20 feet

lenght: 6 feet

c)

width: 6 feet

length: 20 feet

d)

width: 4 feet

length: 30 feet

35.

$y\le-4\left(x-2\right)^2-4$

Which graph matches the inequality

a)

b)

c)

d)

36.

Which graph matches the inequality

y\ge\frac{1}{2}\left(x+1\right)\left(x-3\right)

a)

b)

c)

d)

37.

Solve the inequality algebraically

x^2-8x\le-12

a)

$2\le x\le6$

b)

$-2<x<-6$

c)

$2\ge x\ge6$

d)

$-2\ge x\ge-6$

38.

Solve the inequality

x^2+11x+30\ge0

a)

$x\le-6;\ \ \ x\ge-5$

b)

$x\le-5;\ \ \ x\ge-6$

c)

$x\ge-6;\ \ \ x\ge-5$

d)

$x\le-6;\ \ \ x\le-5$

39.

A shoe manufacturer determines its monthly revenue, R(q), in dollars, where q is the number of pairs of shoes sold each month. How many shoes will the company need to sell to maximize profit? What is the maximum value of the ccompany's revenue?

R\left(q\right)=-.27\left(q-250\right)^2+16,500

a)

-250 shoes; $16,500

b)

16, 500 shoes; $250

c)

250 shoes; $16,500

d)

-16,500 shoes; $250

40.

Let x = a and x = b be the solutions to the equation below. What is the value of -a - b?

\left(3x-2\right)\left(x+5\right)=0

a)

$\frac{13}{3}$

b)

$\frac{17}{3}$

c)

$\frac{2}{3}$

d)

$-5$

Unit 6 Test Review

Total questions: 40

Worksheet time: 2hrs 27mins

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