Free Printable Analyzing Quadratic Functions in Real World

1.

The graph below shows the height, in feet, over time, in seconds, of a student's rocket. Use the graph to answer the questions below. What was the maximum height the rocket reached?

a)

25 feet

b)

45 feet

c)

65 feet

d)

85 feet

2.

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$h\left(x\right)=-4x^2+24x+10$
Part A: What is the starting height of the t-shirt?

a)

24 feet

b)

10 feet

c)

-4 feet

d)

3 feet

3.

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$h\left(x\right)=-4x^2+24x+10$
Part B: After how many seconds does the t-shirt reach its greatest height? Solve algebraically.

a)

3 seconds

b)

46 seconds

c)

5 seconds

d)

10 seconds

4.

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$h\left(x\right)=-4x^2+24x+10$
Part C: What is the t-shirt’s greatest height? Solve Algebraically

a)

24 feet

b)

9 feet

c)

46 feet

d)

34 feet

5.

Analyze the vertex of the quadratic function $y = 3x^2 - 18x + 27$ . What does this vertex represent in a real-world scenario where the graph models the cost of producing $x$ items?

a)

The minimum cost of production

b)

The maximum cost of production

c)

The break-even point of production

d)

The starting cost of production

6.

Analyze the given graph and the determine the correct function. (a) (b)

Choose from the below words

x(x-2)

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

x+(x-2)

$x^2-2$

(x+4)(x+5)

(x-0)

7.

What do the x-intercepts of the quadratic function $y = x^2 - 4x + 3$ represent in a real-world scenario where the graph models the height of a thrown ball over time?

a)

The times at which the ball hits the ground

b)

The maximum height of the ball

c)

The initial height of the ball

d)

The speed of the ball

8.

A quadratic function is used to model the trajectory of a rocket, given by $y = -4.9x^2 + 49x + 0.5$ . What is the significance of the vertex of this parabola in this context?

a)

It represents the launch point of the rocket.

b)

It represents the maximum height the rocket reaches.

c)

It represents the landing point of the rocket.

d)

It represents the total time the rocket is in the air.

9.

A quadratic function models the profit $P$ (in hundreds of dollars) from selling $x$ items, given by $P = -5x^2 + 150x - 1000$ . What is the maximum profit that can be achieved?

a)

$1000$ dollars

b)

$3750$ dollars

c)

$750$ dollars

d)

$1500$ dollars

10.

The path of a soccer ball kicked into the air can be modeled by the quadratic equation $y = -16x^2 + 40x + 0$ . What do the x-intercepts of this equation represent?

a)

The maximum height reached by the ball

b)

The points at which the ball was kicked and caught

c)

The points at which the ball touches the ground

d)

The duration the ball was in the air

11.

Prince is trying to throw a ball over a fence. The height of the ball, in feet based on the number of seconds, is represented by the equation:
$f\left(t\right)=-3.5t^2+14t+3$
Part B: What is the maximum height the ball reached after Prince threw it?

a)

14 feet

b)

17 feet

c)

19 feet

d)

22 feet

12.

Prince is trying to throw a ball over a fence. The height of the ball, in feet based on the number of seconds, is represented by the equation:
$f\left(t\right)=-3.5t^2+14t+3$
Part C: How long will it take for the ball to hit the ground?

a)

Between 1 and 2 seconds

b)

Between 2 and 3 seconds

c)

Between 3 and 4 seconds

d)

Between 4 and 5 seconds

13.

Prince is trying to throw a ball over a fence. The height of the ball, in feet based on the number of seconds, is represented by the equation:
$f\left(t\right)=-3.5t^2+14t+3$
Part D: Prince is trying to throw the ball over a 19 foot high fence. Will his throw make it over?

a)

Yes it will definitely clear 19 feet

b)

No his arm is weak it won't make it over 19 feet

c)

I'm not sure about this one, I've never seen Prince throw

14.

The axis of symmetry of a parabola given by the equation y=ax²+bx+c is given by:

a)

x=−b/2a

b)

y=−b/2a

c)

x=b/a

d)

y=b/a

15.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

16.

Over what interval is this function constant?

a)

(−5, ∞)

b)

(−3, 4)

c)

(4,∞)

d)

(−5)

17.

What is the RANGE?

a)

(-∞, +∞)

b)

(-2, +∞)

c)

[-2, +∞)

d)

(-∞, 0) U (0, +∞)

18.

For what intervals of x is f(x) positive?

a)

x<-2 and x>2

b)

-2<x<2

c)

x≤-2 and x≥2

d)

x≥-4

19.

For what intervals of x is f(x) negative?

a)

-2<x<2

b)

-2≤x≤2

c)

x<-2 and x>2

d)

x≤-4

20.

What is the range of f(x)?

a)

y≥-4

b)

all real numbers

c)

x≥-4

Analyzing Quadratic Functions in Real World

Total questions: 20

Worksheet time: 20mins

Similar Resources on Wayground