Question

Quadratic functions can be used to describe the rate at which an object will fall and predict when it will land or how high it may go. Create a quadratic function using the function y=−16t2
to help predict when an object will return to the ground from being kicked, dropped, or thrown. In 3–5 sentences, describe the scenario in which you will use the function. Write the complete function and explain the meaning of the variable t and the constant value.

Answer 1

Scenario: You throw a baseball straight up from a 5-foot-high balcony with an initial upward speed of 20 feet per second. The height y (in feet) of the ball t seconds after you throw it is modeled by the quadratic function

y = -16t^2 + 20t + 5.

Here t is time in seconds after the throw, y is the height in feet, -16 is half the downward acceleration due to gravity (−32 ft/s^2) which makes the t^2 term negative, 20 is the initial vertical velocity in ft/s, and 5 is the initial height in feet. To predict when the ball returns to the ground, set y = 0 and solve -16t^2 + 20t + 5 = 0 for t (taking the positive root).