Solving Quadratics: Real-Life Applications and Graphing

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, find the dimensions of the garden using the quadratic factored form.

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -5t^2 + 10t + 1.5. When will the ball hit the ground?

• 4 seconds

• 5 seconds

• 3 seconds

• 2 seconds

The product of two consecutive integers is 72. Find the integers by setting up a quadratic equation in factored form.

• The integers are 8 and 9.

• 6 and 7

• 7 and 8

• 9 and 10

A company produces x units of a product, and the profit P in dollars can be modeled by the equation P(x) = -2(x - 10)(x - 20). Determine the number of units that should be produced to maximize profit.

• 25

• 20

• 10

• 15

A projectile is launched from the ground with an initial velocity of 20 m/s. The height h in meters after t seconds is given by h(t) = -5t^2 + 20t. Graph the function and determine the time when the projectile reaches its maximum height.

• 3 seconds

• 1 second

• 2 seconds

• 4 seconds

The width of a rectangular pool is 2 meters less than its length. If the area of the pool is 48 square meters, find the dimensions of the pool using a quadratic equation in factored form.

• Length: 6 meters, Width: 4 meters

• Length: 8 meters, Width: 6 meters

• Length: 10 meters, Width: 8 meters

• Length: 7 meters, Width: 5 meters

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is represented as x meters, express the area A in terms of x and find the dimensions that maximize the area using quadratic factored form.

• Length = 25 meters, Width = 25 meters

• Length = 50 meters, Width = 0 meters

• Length = 40 meters, Width = 10 meters

• Length = 30 meters, Width = 20 meters

The height of a parabolic arch is modeled by the equation h(x) = -x^2 + 4x + 5, where x is the distance from the center. Find the maximum height of the arch and the distance from the center at which it occurs.

• Maximum height: 7, Distance from center: 1

• Maximum height: 8, Distance from center: 3

• Maximum height: 9, Distance from center: 2

• Maximum height: 6, Distance from center: 4

A toy rocket is launched from the ground. Its height in meters after t seconds is given by the equation h(t) = -4.9t^2 + 20t. Determine when the rocket will reach its maximum height and how high it will go.

• The rocket will reach its maximum height at 1.5 seconds, and the maximum height will be 15 meters.

• The rocket will reach its maximum height at 2.04 seconds, and the maximum height will be 20.4 meters.

• The rocket will reach its maximum height at 2 seconds, and the maximum height will be 18 meters.

• The rocket will reach its maximum height at 3 seconds, and the maximum height will be 25 meters.

The area of a triangular plot of land is 60 square meters. If the base is 4 meters longer than the height, find the dimensions of the plot using a quadratic equation in factored form.

• Height: 10 meters, Base: 14 meters

• Height: 5 meters, Base: 9 meters

• Height: 8 meters, Base: 12 meters

• Height: 6 meters, Base: 10 meters