Free Printable 3rd Monthly Assessments (Grade9) (Quadratic Function, Variation)

1.

Given the equation $y=3\left(x+5\right)^{2\ }-4$ , what is the vertex of the parabola?

a)

(-5,4)

b)

(-15,-4)

c)

(-5,-4)

d)

(15,-4)

2.

Convert to vertex form $h(x)=x^2-6x+7.$

a)

$h(x)=(x-3)^2-2$

b)

$h(x)=(x+3)^2-2$

c)

$h(x)=(x-3)^2+2$

d)

$h(x)=(x+3)^2+2$

3.

Describe the transformations of $f\left(x\right)$ when compared to the parent function:

$f(x)=x^2+5$ .

a)

horizontal shift right 5 units

b)

vertical shift up 5 units

c)

horizontal shift left 5 units

d)

vertical shift down 5 units

4.

What is the axis of symmetry for the following question $y=4x^2-8x+9?$

a)

$x=-8$

b)

$x=-1$

c)

$x=1$

d)

$x=2$

5.

Which equation best represents the graph?

a)

$y=2(x-4)^2+5$

b)

$y=-2(x-4)^2+5$

c)

$y=2(x+4)^2+5$

d)

$y=-2(x+4)^2+5$

6.

What is the turning point of the parabola?

a)

parabola

b)

vertex

c)

axis of symmetry

d)

roots

7.

What is the vertex of the function $f(x)=(x+3)^2-2?$

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

8.

Which table of values represent the quadratic function: $f\left(x\right)=2\left(x+1\right)^{2\ }-4$

a)

b)

c)

d)

9.

What is the vertex of $f(x)=x^2-12x+38?$

a)

(6,2)

b)

(-5,123)

c)

(5,3)

d)

(-6,156)

10.

Compare the stretching of the graphs from narrower to wider.

a. $f\left(x\right)=2x^{2\ }+3x+1$ ; b. $f\left(x\right)=5x^{2\ }-4x+1$ ; c. $f\left(x\right)=\frac{1}{3}x^2+5x$

a)

a, b, c

b)

b,c,a

c)

a,c,b

d)

b,a,c

11.

In quadratic function $f\left(x\right)=ax^2+bx+c$ , how does the sign of the leading coeffient " $a$ " affects the parabola?

a)

vertical shifting

b)

horizontal shifting

c)

opening

d)

stretching

12.

Which of the following is the transformation of the graph of $f\left(x\right)=-2\left(x+3\right)^{2\ }+3$ ?

a)

OPENING: downward

shifts:3 units left, 3 units up

Stretching: narrower than $f\left(x\right)=x^{2\ }$

b)

OPENING: downward

SHIFTS: 3 units right, 3 units up

STRETCHING: wider than $f\left(x\right)=x^{2\ }$

c)

OPENING: downward

SHIFTS: 3 units left, 3 units down,

STRETCHING: wider than $f\left(x\right)=x^{2\ }$

d)

OPENING: upward

SHIFTS: 3 units left, 3 units down,

STRETCHING: narrower than $f\left(x\right)=x^{2\ }$

13.

Which of the following is the transformation of the graph of $f\left(x\right)=\frac{1}{2}\left(x-7\right)^{2\ }-1$ ?

a)

OPENING: upward

shifts: 7 units right, 1 unit down

Stretching: wider than $f\left(x\right)=x^{2\ }$

b)

OPENING: downward

SHIFTS: 7 units left, 1 unit up

STRETCHING: wider than $f\left(x\right)=x^{2\ }$

c)

OPENING: downward

SHIFTS: 3.5 units up, 1 unit down

STRETCHING: narrower than $f\left(x\right)=x^{2\ }$

d)

OPENING: downward

SHIFTS: 7 units right, 1 unit down

STRETCHING: wider than $f\left(x\right)=x^{2\ }$

14.

Which of the following is the general form of the quadratic function given vertex (2,-3) and $a=-3$ ?

a)

$f\left(x\right)=-3x^2+12x-15$

b)

$f\left(x\right)=3x^2-12x-9$

c)

$f\left(x\right)=-3x^2+12x+15$

d)

$f\left(x\right)=3x^2+12-3$

15.

What is the turning point of the parabola given the general form $𝑓(𝑥)=−3𝑥^2−30𝑥−75$ ?

a)

(-5,0)

b)

(-6,5)

c)

$\left(-10,0\right)$

d)

$\left(5,0\right)$

16.

y varies inversely as x. y = 3 when x = 9. Determine the inverse variation equation.

a)

y=27/x

b)

x=27/y

c)

y=27x

d)

x=27y

17.

Which equation represents inverse variation between x and z.

a)

$x=\frac{y}{z}$

b)

$x=-\frac{3z}{y}$

c)

$z=-\frac{3y}{z}$

d)

$xy=5y$

18.

Which of these graphs show a direct relationship between x and y?

a)

b)

c)

d)

19.

The time, $t$ , required to empty a tank varies inversely as the rate, $r$ , of pumping. If a pump can empty a tank in 2.5 hours at a rate of 400 gallons per minute, how long will it take to empty a tank at 500 gallons per minute?

a)

1 hour

b)

1.5 hours

c)

2 hours

d)

3 hours

20.

The number of words Maria typed varied directly with the amount of time she spent typing. If she typed 275 words in 5 minutes, how long would it take her to type 1,100 words?

a)

220 minutes

b)

15 minutes

c)

20 minutes

d)

4 minutes

21.

The gas pressure in a chamber varies directly with the temperature in the chamber. If the pressure in the chamber is 150 atmospheres (atm) when the chamber is at 50 degrees, what is the pressure in the chamber when the temperature of the chamber is 75 degrees?

a)

175 atm

b)

225 atm

c)

200 atm

d)

275 atm

22.

In item number 21, which graph shows inverse variation between two quantities?

a)

b)

c)

d)

23.

y varies directly as x such that, when x=10, y=4. Find y, when x=15.

a)

6

b)

4

c)

9

d)

10

24.

Is your heartbeat a constant or a variable quantity? Explain.

a)

A variable, since it varies from person to person.

b)

A constant, since the heart supplies a constant amount of blood to the body.

c)

A variable, since it varies depending on the kind of activity that a person does.

d)

A constant, since the heart beats constantly every day, no matter what the activity

25.

y varies inversely as x such that, when x=12, y=9. Find y, when x=27.

a)

3

b)

9

c)

4

d)

18

26.

Does your watch tick faster or slower as your activity varies? Why or why not?

a)

Yes, the more I am active, the faster it ticks.

b)

No, the speed of the ticking of the watch is a constant quantity.

c)

Yes, the less active I am, the slower it ticks.

d)

No, the speed of the ticking of the watch is determined by the quality of the watch.

27.

How does the area of a rectangle vary in its length and width?

a)

directly

b)

jointly

c)

inversely

d)

indirectly

28.

In which activity would your heart beat the fastest?

a)

walking

b)

eating

c)

sleeping

d)

running

29.

Determine if the relationship between the two quantities is a direct variation.

a)

This is a direct variation since the graph passes through the origin and the ratio of the number of miles to the number of hours is constant.

b)

This is not a direct variation since the graph does not pass through the origin and the ratio of the number of miles to the number of hours is not constant.

c)

This s a direct variation since the graph is a straight line and the ratio of the number of miles to the number of hours is constant

d)

This is not a direct variation since the graph is not a straight line and the ratio of the number of miles to the number of hours is not constant.

30.

"It is a virtue that keeps a person’s determination to achieve goals despite the difficulties and challenges that come along the way."

a)

Natural Moral Law

b)

Conscience

c)

Prudence

d)

Perseverance

3rd Monthly Assessments (Grade9) (Quadratic Function, Variation)

Total questions: 30

Worksheet time: 15mins

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