Quadratic Function Word Problems

A model rocket was launched from the ground. The path of the rocket can be modeled by a quadratic function. The vertex of the parabola was (12, 72). What does the y-coordinate represent?

• the horizontal distance the rocket traveled

• the maximum height of the rocket

• the starting point of the rocket

• how fast the rocket was travelling

The height of a ball Doreen tossed into the air can be modeled by the function h(x) = −4.9x² + 6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents:

• the initial height of the ball

• the time at which the ball reaches the ground

• the time at which the ball was at its highest point

• the maximum height the ball attained when thrown in the air

The height, f(x), of a ball tossed into the air can be represented by the equation

f(x) = −x² + 10x + 3, where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?

• y = 5

• y = -5

• x = 5

• x = -5

Fireworks are fired from the roof of a 100-foot building. The equation h(t) = -16t² +84t + 100 models the height, h(t), of the fireworks at any given time, t. How high do the fireworks get?

• 2.625 ft

• 6.25 ft

• 100 ft

• 210.25 ft

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h(t) = -4t² + 12t. How high did the soccer ball get?

• 1.5 ft

• 3 ft

• 15 ft

• 9 ft

A frog is sitting on the ground when he is scared by a big dog. The movement of the frog is modeled by the equation

h(t) = -6t² + 6t where h(t) is the frog's height at any given time, t. How high does the frog jump?

• 0.5 ft

• 1 ft

• 1.5 ft

• 2 ft

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

• 0.25 ft

• 24 ft

• 25 ft

• 8 ft

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p(t) = -15x² + 600x + 60

What is the maximum profit you can make from selling tickets?

• $6060

• $20

• $600

• $10,250

The equation f(t) = -4.9t² + 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. What is the initial height of the rocket?

• 0 m

• 2 m

• 4.9 m

• 50 m