Real-World Applications of the Quadratic Formula

A rectangular garden has an area of 144 square meters. If the length of the garden is 12 meters, what is the width? Use the quadratic formula to find the width.

• 16 meters

• 14 meters

• 12 meters

• 10 meters

A ball is thrown upwards from a height of 5 meters with an initial velocity of 20 meters per second. The height of the ball after t seconds is given by the equation h(t) = -5t^2 + 20t + 5. How long will it take for the ball to hit the ground?

• 3.5 seconds

• 5.0 seconds

• 4.24 seconds

• 6.8 seconds

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 20t + 10. Find the time when the projectile reaches a height of 0 meters using the quadratic formula.

• t = (20 - √596) / -9.8, approximately 0.5 seconds or t = (20 + √596) / -9.8, approximately 4.1 seconds.

• t = (20 - √400) / -9.8, approximately 2.0 seconds

• t = (20 + √500) / -9.8, approximately 3.0 seconds

• t = (20 - √500) / -9.8, approximately 1.0 seconds

A rectangular pool has a length that is 3 meters longer than its width. If the area of the pool is 70 square meters, what are the dimensions of the pool? Use the quadratic formula to find the width and length.

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -2x^2 + 40x - 50. How many items should the company sell to maximize profit? Use the quadratic formula to find the number of items.

• 5

• 20

• 15

• 10

The height of a triangle is 4 meters less than its base. If the area of the triangle is 48 square meters, what are the dimensions of the triangle? Use the quadratic formula to find the base and height.

• Base: 10 meters, Height: 6 meters

• Base: 12 meters, Height: 8 meters

• Base: 14 meters, Height: 10 meters

• Base: 16 meters, Height: 12 meters

A car's distance from a starting point can be modeled by the equation d(t) = 2t^2 + 3t + 5. How long will it take for the car to be 25 meters away from the starting point? Use the quadratic formula to solve for t.

• 4.5 seconds

• 2.5 seconds

• 3.0 seconds

• 1.5 seconds

The area of a square is represented by the equation A = x^2. If the area is 64 square meters, what is the length of one side of the square? Use the quadratic formula to find x.

• 10

• 12

• 6

• 8

A farmer has a rectangular field with a perimeter of 100 meters. If the length is 10 meters more than the width, what are the dimensions of the field? Use the quadratic formula to find the width and length.

• Width: 30 meters, Length: 40 meters

• Width: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 35 meters

• Width: 15 meters, Length: 25 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. How long will it take for the projectile to reach the ground? Use the quadratic formula to find the time.

• 5 seconds

• 4 seconds

• 2 seconds

• 3 seconds