# Lesson Worksheet: Applications of Quadratic Equations Mathematics

In this worksheet, we will practice solving word problems by forming and solving quadratic equations.

**Q1: **

A cannon is fired on a field, and the height of the projectile seconds after firing is meters off the ground, where .

Find the time taken for the projectile to hit the ground.

Find the maximum height of the projectile.

**Q2: **

The diagram shows part of a suspension bridge fastened onto two supports at the same height off the ground on both sides.

The height, meters, of the suspension bridge from the ground is modeled by the equation , where is the horizontal distance from the left support in meters.

Find the maximum height, in meters, of the suspension bridge from the ground.

Find the minimum height, in meters, of the suspension bridge from the ground.

**Q3: **

A mass is dropped off the Leaning Tower of Pisa. The height, meters, of the mass after seconds is modeled by the equation .

Find the height of the Leaning Tower of Pisa.

Find the time taken for the mass to hit the ground. Give your answer to two decimal places.

**Q4: **

The sum of a positive number and twice its square is 253. Find the positive number .

**Q5: **

The diagram shows an entrance to a tunnel with a parabolic arch connecting two straight vertical sections of a wall of equal height.

The height of the tunnel in meters at meters from the left wall is given by the equation .

Find the height of the straight vertical section of the wall.

Find the total width of the arch.

Find the maximum height of the arch.

- A m
- B m
- C m
- D m
- E m

**Q6: **

A city council wants to add a diagonal path to a rectangular park. The length of the diagonal path will be 26 m and the sum of the lengths of the sides of the park is 34 m.

Find the dimensions of the park.

- A and
- B and
- C and
- D and
- E and

**Q7: **

The value of a vintage car in pounds years after the year 1980 is given by the equation .

What is the value of the car in 1980?

How many years after 1980 does it take for the car to reach its original value?

How many years after 1980 does the value of the car reach its lowest value?

**Q8: **

A farm owner can model the profit in pounds that they will make in a day selling liters of milk using the equation .

How much money will the farm owner lose if they sell no milk?

- A
- B
- C
- D
- E

How many liters of milk do they need to sell to break even?

**Q9: **

A farmer has 100 m of fencing and wants to fence off the largest possible rectangular field he can. Find the area of the largest rectangular field possible that can be fenced off with 100 m of fencing.

**Q10: **

A ball is thrown from a building and its height in meters seconds after being thrown follows the quadratic equation . The building is 40 m tall. The maximum height of the ball off the ground is 44 m and this height is reached after 2 s.

Find the values of and .

- A and
- B and
- C and
- D and
- E and