Quiz about Quadratic Modeling Lesson

Question 1

Which of the following is vertex form of a quadratic equation?

Accepted Answer

y = a(x - h)² + k

Answer

y = a(x - p)(x - q)

Answer

y = a(x - h)² - k

Answer

y = a(x + h)² + k

Question 2

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

Accepted Answer

(0,3)

Answer

(3,0)

Answer

(0,2)

Answer

y=8

Question 3

Where is the AoS (Axis of Symmetry) for
y = 2x²+4x+2

Accepted Answer

x = -1

Answer

x = 2

Answer

x = 1

Answer

x = 4

Question 4

Is this point a max or min?

Accepted Answer

max

Answer

min

Question 5

Find the vertex of the quadratic:
y = -2x² + 4x + 3

Accepted Answer

(1, 5)

Answer

(0, 3)

Answer

(-1, 5)

Answer

(1, -5)

Question 6

What is the vertex of the graph?

Accepted Answer

(3, -1)

Answer

(2, 4)

Answer

(0, 8)

Answer

(4, 2)

Question 7

What is the vertex of y= x²- 8x + 14 ?

Accepted Answer

(4, -2)

Answer

(2, 4)

Answer

(-4, -2)

Answer

(-2, 4)

Question 8

What does

x=-b/2a find?

Accepted Answer

axis of symmetry

Answer

vertex

Answer

y-intercept

Answer

slope

Question 9

Does the equation open or or down?
Y = -3x² +7x - 2

Accepted Answer

down

Answer

up

Question 10

Solve
a² + 2a - 24 = 0

Accepted Answer

a = -6, 4

Answer

a = 6, -4

Answer

a = 12, -2

Answer

a = 8, -3

Question 11

What is the vertex of
f(x) = (x - 1)² + 2?

Accepted Answer

(1, 2)

Answer

(-1, 2)

Answer

(-1, -2)

Answer

(1, -2)

Question 12

Which of the following equations matches standard form of a quadratic?

Accepted Answer

y = ax² + bx + c

Answer

ax + by = c

Answer

y = a(x - h)² + k

Answer

y = mx + b

Question 13

Use the graph to determine the solutions.

Accepted Answer

1 and 3

Answer

-1 and -3

Answer

1 and -3

Answer

-1 and 3

Question 14

How many real solutions does this quadratic have?

Accepted Answer

two solutions

Answer

no real solutions

Answer

one solution

Answer

three solutions

Question 15

What are the solutions for this graph?

Accepted Answer

{0, 8}

Answer

{ 0, -8}

Answer

{4, 80}

Answer

no real solution

Question 16

Solve the equation (x+5)(x-10)=0

Accepted Answer

{-5, 10}

Answer

{5, -10}

Answer

x2-5x-50

Answer

no solution

Question 17

What should you do first in solving this equation?
x² + 6x - 13 = 3

Accepted Answer

Make it equal 0 by subtracting 3 on each side

Answer

Get factored form

Answer

Write down: a=1, b=6, c=-13

Answer

Type it all in a calculator.

Question 18

No Calculator: Find the axis of symmetry and vertex.
$$y=-x^2+10x-28$$

Accepted Answer

Axis of Symmetry: x = 5
Vertex: (5, -3)

Answer

Axis of Symmetry: x = 10
Vertex: (10, -28)

Answer

Axis of Symmetry: x = -5
Vertex: (-5, -103)

Answer

Axis of Symmetry: x = 5
Vertex: (5, 47)

Question 19

Select all the potential factors of the given graph.

Accepted Answer

(x+3)

Accepted Answer

(x-8)

Answer

(x-3)

Answer

(x+8)

Answer

x

Question 20

What is the equation for axis of symmetry?

Accepted Answer

x=3

Answer

y=3

Answer

x=5

Answer

x=1

Question 21

What is the vertex of the parabola:
y = -12x + 22 + 2x²

Accepted Answer

(3,4)

Answer

(-3,4)

Answer

(3, -4)

Answer

(-3,-4)

Question 22

Solve: x² + 3x - 18 = 0

Accepted Answer

x = 3 and x = -6

Answer

x = -3 and x = 6

Answer

x = -9 and x = 2

Answer

x = 9 and x = -2

Question 23

What are the green dots called?

Accepted Answer

roots or x-intercepts

Answer

axis of symmetry

Answer

vertex

Answer

parabola

Question 24

What is the green dot on the parabola called?

Accepted Answer

maximum

Answer

minumum

Answer

roots

Answer

zeros

Question 25

Solve by factoring: 2x² - 5x - 12 = 0

Accepted Answer

x = 4 and x = -3/2

Answer

x = -4 and x = -6

Answer

x = 4 and x = 6

Answer

x = -4 and x = 3/2

Question 26

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

Accepted Answer

(-5, -4)

Answer

(5, -4)

Answer

(-15, -4)

Answer

(15, -4)

Question 27

Which function has the same vertex as y = x² + 4x - 1?

Accepted Answer

y = (x + 2)² - 5

Answer

y = (x - 2)² + 5

Answer

y = (x + 2)² - 1

Answer

y = (x +2)² + 3

Question 28

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

Accepted Answer

x=1

Answer

x=-6

Answer

x=2

Answer

x=-1

Question 29

Solve
x² + 2x - 24 = 0

Accepted Answer

x = -6, x = 4

Answer

x = 6, x = -4

Answer

x = 12, x = -2

Answer

x = 8, x = -3

Question 30

Solve
x² + 9x + 20 = 0

Accepted Answer

x = -4, x = -5

Answer

x = -2, x = -10

Answer

x = -3, x = -4

Answer

x = -4, x = -6

Question 31

How high would you jump if the equation for jumping from a cliff is:
h(t) = -16t² + 8t + 24?

Accepted Answer

25

Answer

24

Answer

8

Answer

26

Question 32

At what time would you reach 16 ft above the water if you jump of a cliff using the formula:
h = -16t² + 8t + 24?

Accepted Answer

1

Answer

8

Answer

1/2

Answer

1/4

Question 33

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

Accepted Answer

(-2, 16)

Answer

(-2, 14)

Answer

(2, 4)

Answer

(-2, 4)

Question 34

Question 34.

Accepted Answer

2.225 seconds

Answer

8 seconds

Answer

2.5 seconds

Answer

2.5 seconds

Question 35

Question 35.

Accepted Answer

24 ft

Answer

8 ft

Answer

12 ft

Answer

10 ft

Question 36

Question 36.

Accepted Answer

10 seconds

Answer

16 seconds

Answer

8 seconds

Answer

14 seconds

Question 37

Question 37.

Accepted Answer

256 ft

Answer

240 ft

Answer

265 ft

Answer

230 ft

Question 38

Determine the vertex for y = 5x²- 20x + 13

Accepted Answer

(2, -7)

Answer

(5, -7)

Answer

(-2, -7)

Answer

(-7, -2)

Question 39

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

Accepted Answer

$6060

Answer

$20

Answer

$600

Answer

$10,250

Question 40

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t²+ 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

Accepted Answer

1 second

Answer

0.5 seconds

Answer

1.5 seconds

Answer

2 seconds

Answer

3 seconds

Question 41

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t² + 80

About how long did it take for the balloon to hit the ground?

Accepted Answer

2.24 seconds

Answer

1.73 seconds

Answer

2.45 seconds

Answer

2.83 seconds

Question 42

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

Accepted Answer

1.25 seconds

Answer

1.4 seconds

Answer

2.5 seconds

Answer

2 seconds

Question 43

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t² + 45

When is the ball at ground level?

Accepted Answer

only at t = 3 seconds

Answer

only at t = 0 seconds

Answer

only at t = 9 seconds

Answer

at both t = 0 seconds and t = 3 seconds

Question 44

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

Accepted Answer

0.50 seconds

Answer

0.1 seconds

Answer

0.25 seconds

Answer

0.75 seconds

Answer

1 second

Question 45

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?

Accepted Answer

210.25

Answer

2.625

Answer

6.25

Answer

100

Answer

200

Question 46

Your cousin hit a golf ball with an initial velocity of 27 feet per second. The equation h = -6t² + 27t models the golf ball's height in feet t seconds after the ball was hit. How long after being hit did the ball reach maximum height?

Accepted Answer

2.25 seconds

Answer

1 second

Answer

3 seconds

Answer

4.5 seconds

Answer

5 seconds

Question 47

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t² + 12t. How high did the soccer ball get?

Accepted Answer

9

Answer

1.5

Answer

3

Answer

5

Answer

15

Question 48

Which of the following mean the same as x-intercept? (More than one answer! Select all that are correct)

Accepted Answer

Zero

Accepted Answer

Root

Accepted Answer

Solution

Answer

Axis of Symmetry

Answer

Maximum

Question 49

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

Accepted Answer

9 seconds

Answer

4 seconds

Answer

-2 seconds

Answer

-6 seconds

Question 50

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

Accepted Answer

5 seconds

Answer

1 second

Answer

2 seconds

Answer

3 seconds

Question 51

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

Accepted Answer

2 meters

Answer

5 meters

Answer

40 meters

Answer

20 meters

Question 52

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t
When will the object reach its maximum height?

Accepted Answer

4 seconds

Answer

4 ft

Answer

0 seconds

Answer

0 ft

Question 53

Solve the word problem: How fast would you reach the water if you jump of a cliff using the formula: h(t) = -16t² + 8t + 24?

Accepted Answer

1.5

Answer

8

Answer

1

Answer

1/4

Question 54

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t²+ 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

Accepted Answer

5.625 sec

Answer

126.56 ft

Answer

2.81 sec

Answer

0 ft

Question 55

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

Accepted Answer

0.25 seconds

Answer

0.1 seconds

Answer

0.50 seconds

Answer

1 second

Answer

2 seconds

Question 56

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

Accepted Answer

8 feet

Answer

1 foot

Answer

5 feet

Answer

7 feet

Answer

12 feet

Question 57

What is the equation of this graph?

Accepted Answer

f(x) = (x - 1)² - 5

Answer

f(x) = (x -5)² + 1

Answer

f(x) = (x + 1)² - 5

Answer

f(x) = (x + 5)² +1

Question 58

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

Accepted Answer

(-5, -4)

Answer

(5, -4)

Answer

(-15, -4)

Answer

(15, -4)

Question 59

Identify the vertex and whether the graph opens up or down.

Accepted Answer

(-5, 2); opens up

Answer

(5, 2); opens up

Answer

(5, 2); opens down

Answer

(-5, 2); opens down

Question 60

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

Accepted Answer

x = -3

Answer

y = -2

Answer

x = 3

Answer

y = 2

Question 61

Which equation has a vertex of (-3, 4)?

Accepted Answer

y = 2(x+3)²+ 4

Answer

y = (x+3)² - 4

Answer

y = (x-3)² + 4

Answer

y = 2(x - 3)² + 4

Question 62

What is the axis of symmetry of the given function?

Accepted Answer

x = 1

Answer

y = 1

Answer

y = -1

Answer

x = -1

Question 63

What is the vertex of the parabola: y=2(x-3)²+4

Accepted Answer

(3,4)

Answer

(-3,4)

Answer

(3, -4)

Answer

(-3,-4)

Question 64

Find the vertex. y = x²+ 16x + 71

Accepted Answer

V(-8, 7)

Answer

V(-8, 3)

Answer

V(8, 10)

Answer

V(16, -2)

Quadratic Modeling Lesson

110 questions

Which of the following is vertex form of a quadratic equation?

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

Where is the AoS (Axis of Symmetry) for
y = 2x²+4x+2

Is this point a max or min?

Find the vertex of the quadratic:
y = -2x² + 4x + 3

What is the vertex of the graph?

What is the vertex of y= x²- 8x + 14 ?

What does
x=-b/2a find?

Does the equation open or or down?
Y = -3x² +7x - 2

Solve
a² + 2a - 24 = 0

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Quadratic Modeling Lesson

110 questions

Which of the following is vertex form of a quadratic equation?

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

Where is the AoS (Axis of Symmetry) for y = 2x2+4x+2

Is this point a max or min?

Find the vertex of the quadratic:y = -2x2 + 4x + 3

What is the vertex of the graph?

What is the vertex of y= x2 - 8x + 14 ?

What does x=-b/2a find?

Does the equation open or or down? Y = -3x2 +7x - 2

Solve a2 + 2a - 24 = 0

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

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

Where is the AoS (Axis of Symmetry) for
y = 2x²+4x+2

Find the vertex of the quadratic:
y = -2x² + 4x + 3

What is the vertex of y= x²- 8x + 14 ?

What does
x=-b/2a find?

Does the equation open or or down?
Y = -3x² +7x - 2

Solve
a² + 2a - 24 = 0