Solving Quadratics: Dimensions & Graphs with Solutions

A rectangular garden has an area of 144 square meters. If the length is twice the width, find the dimensions of the garden by solving the quadratic equation. Check for extraneous solutions.

• Width: 10 meters, Length: 20 meters

• Width: 8 meters, Length: 16 meters

• Width: 6√2 meters, Length: 12√2 meters

• Width: 4√2 meters, Length: 8√2 meters

A ball is thrown upwards from a height of 16 meters with an initial velocity of 24 meters per second. How long will it take for the ball to hit the ground? Solve the quadratic equation and check for extraneous solutions.

• 7.50 seconds

• 4.75 seconds

• 6.00 seconds

• 5.25 seconds

The area of a square is represented by the equation x^2 = 49. What is the length of one side of the square? Remember to check for extraneous solutions.

• 7

• 5

• 14

• 0

A car's height above the ground can be modeled by the equation h(t) = -4.9t^2 + 20t + 5, where t is time in seconds. At what time will the car reach the ground? Solve the quadratic equation and graph the function to visualize the height over time.

• Approximately 4.47 seconds

• Approximately 5.2 seconds

• Approximately 3.5 seconds

• Approximately 6.0 seconds

A swimming pool is being filled with water. The volume of water in the pool can be modeled by the equation V = x^2 + 10x, where V is the volume in cubic meters. If the volume is 60 cubic meters, find the dimensions of the pool by solving the quadratic equation. Check for extraneous solutions.

• The dimensions of the pool are 5 meters and 12 meters.

• The dimensions of the pool are 3 meters and 15 meters.

• The dimensions of the pool are approximately 4.22 meters and 14.22 meters.

• The dimensions of the pool are 6 meters and 10 meters.

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. Determine the time when the projectile reaches a height of 0 meters. Solve the quadratic equation and graph the function to show the height over time.

• 3 seconds

• 2 seconds

• 4 seconds

• 5 seconds

A rectangular field has a perimeter of 100 meters. If the length is 5 meters more than the width, find the dimensions of the field by solving the quadratic equation. Check for extraneous solutions.

• Width: 30 meters, Length: 35 meters

• Width: 15 meters, Length: 20 meters

• Width: 22.5 meters, Length: 27.5 meters

• Width: 20 meters, Length: 25 meters

The area of a triangle is given by the equation A = 1/2 * base * height. If the area is 36 square meters and the base is represented by the equation b^2 = 36, find the height of the triangle. Solve the quadratic equation and check for extraneous solutions.

• 24

• 12

• 18

• 6

A square's area is represented by the equation x^2 = 64. What is the length of one side of the square? Remember to check for extraneous solutions and graph the function to visualize the area.

• 10

• 12

• 8

• 6

A projectile is launched from a height of 50 meters with an initial velocity of 20 meters per second. How long will it take for the projectile to hit the ground? Solve the quadratic equation and graph the function to visualize the height over time.

• Approximately 5.77 seconds

• Approximately 3.5 seconds

• Approximately 7.2 seconds

• Approximately 4.1 seconds