Quadratic Equations Real World Scenarios

The graph represents the height of a baseball, h, in feet as a function of time, t, in seconds after it was hit by a baseball player. Approximately how many seconds does it take for the ball to hit the ground again?

• ~ -0.1 seconds

• ~ 2 seconds

• ~ 68 seconds

• ~ 4.1 seconds

The equation represents the height of a frog, h, in meters as a function of time, t, in seconds after it jumps out of a tree into a pond. What are the t-intercepts (x-intercepts) of this function?

• (-1,0), (5,0)

• (1,0), (-5,0)

• (0,-1), (0,5)

• (0,1), (0,-5)

The equation represents the height of a frog, h, in meters as a function of time, t, in seconds after it jumps out of a tree into a pond. What is the t-value of the vertex? (Hint this is halfway between the two intercepts)

• 3

• 2

• 2.5

• 0

• ~50.2

• ~40.5

• ~2

• ~44.1

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds. When is the ball at ground level?

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = –16t² + 16t + 480, where t is the time in seconds and h is the height in feet. How long does it take Jason to hit the water?

• -16 seconds

• -6 seconds

• 0 seconds

• 6 seconds

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation: h = -16t² + 80 About how long did it take for the balloon to hit the ground?

• 1.73 seconds

• 2.24 seconds

• 2.45 seconds

• 2.83 seconds

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation: h = -16t^2 + 80 About how long did it take for the balloon to hit the ground?

• 1.73 seconds

• 2.24 seconds

• 2.45 seconds

• 2.83 seconds

A scientist dropped an object from a height of 200 feet. She recorded the height of the object in 0.5-second intervals. Her data is shown.

Based on a quadratic curve of best fit, at what time (in seconds) will the object have a height of 55 feet?

Mathematical Equivalence

OFF

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

• 8 seconds

• 1 second

• 1.5 seconds

• 1/4 second