Mastering Quadratic Equations: Identify & Solve Challenges

A ball is thrown upwards from a height of 2 meters with an initial velocity of 10 m/s. Write the quadratic equation that models the height of the ball over time.

• h(t) = -4.905t^2 + 5t + 2

• h(t) = -4.9t^2 + 10t + 5

• h(t) = -4.905t^2 + 10t + 2

• h(t) = -9.81t^2 + 10t + 2

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 20t + 5. Identify the coefficients of the quadratic equation and explain their significance.

• -4.9 (initial height), 20 (acceleration), 5 (initial velocity)

• The coefficients are -4.9 (acceleration), 20 (initial velocity), and 5 (initial height).

• -4.9 (initial velocity), 20 (initial height), 5 (time)

• -4.9 (initial velocity), 20 (height), 5 (acceleration)

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, write a quadratic equation to find the dimensions of the garden.

• w^2 + 3w + 70 = 0

• w^2 - 3w + 70 = 0

• w^2 + 3w - 70 = 0

• w^2 - 3w - 70 = 0

A car's profit, P, can be modeled by the equation P(x) = -2x^2 + 12x - 16, where x is the number of cars sold. Determine the number of cars sold that maximizes the profit.

• 2

• 5

• 3

• 4

The height of a water fountain can be modeled by the equation h(t) = -5t^2 + 20t, where h is the height in meters and t is the time in seconds. Solve for t when the fountain reaches a height of 15 meters.

• t = 4 seconds

• t = 1 seconds and t = 3 seconds

• t = 2 seconds

• t = 0 seconds

The area of a triangular park is given by the equation A = 0.5 * base * height. If the height is 2 meters more than the base, express the area as a quadratic equation and find the dimensions that maximize the area.

• Base = 2 meters, Height = 4 meters

• Base = 4 meters, Height = 6 meters

• Base = 1 meter, Height = 3 meters

• Base = 3 meters, Height = 5 meters

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, write a quadratic equation to find the dimensions of the pool.

• w^2 + 100 = 0

• w^2 - 50 = 0

• 2w^2 - 200 = 0

• w^2 - 100 = 0

A company finds that its revenue R can be modeled by the equation R(x) = -3x^2 + 30x, where x is the number of units sold. Determine the number of units that should be sold to maximize revenue.

• 3

• 10

• 5

• 7