Quiz about Real World Quadratic Functions

Question 1

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?

Accepted Answer

The times at which the ball hits the ground

Answer

The maximum height of the ball

Answer

The initial height of the ball

Answer

The speed of the ball

Question 2

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?

Accepted Answer

12500 dollars

Answer

$$1000$$ dollars

Answer

$$750$$ dollars

Answer

$$1500$$ dollars

Question 3

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?

Accepted Answer

The points at which the ball touches the ground

Answer

The maximum height reached by the ball

Answer

The points at which the ball was kicked and caught

Answer

The duration the ball was in the air

Question 4

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?

Accepted Answer

The minimum cost of production

Answer

The maximum cost of production

Answer

The break-even point of production

Answer

The starting cost of production

Question 5

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?

Accepted Answer

It represents the maximum height the rocket reaches.

Answer

It represents the launch point of the rocket.

Answer

It represents the landing point of the rocket.

Answer

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

Question 6

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does the rock hit the ground?

Accepted Answer

4.393 seconds

Answer

1.094 seconds

Answer

174.141 seconds

Answer

155 seconds

Question 7

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. How long does it take the rock to reach its maximum height?

Accepted Answer

1.094 seconds

Answer

174.141 seconds

Answer

155 seconds

Answer

4.393 seconds

Question 8

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the height of the cliff?

Accepted Answer

155 ft

Answer

1.094 ft

Answer

174.141 ft

Answer

4.393 ft

Question 9

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the maximum height the rock reaches ?

Accepted Answer

174.141 ft

Answer

1.094 ft

Answer

155 ft

Answer

4.393 ft

Question 10

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?

Accepted Answer

65 feet

Answer

25 feet

Answer

45 feet

Answer

85 feet

Question 11

Mrs. Martone's 7th grade science class built and launched rockets. 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. When the rocket was at 15 feet, how many seconds passed by?

Accepted Answer

seconds

Answer

14 seconds

Answer

7 second

Answer

It was never at 15 feet

Question 12

A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds. For which interval is the ball's height always decreasing?

Accepted Answer

$$2.5<x<5.5$$

Answer

$$0\le x\le2.5$$

Answer

$$0<x<5.5$$

Answer

$$x\ge2$$

Question 13

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

Real World Quadratic Functions

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