Question

an athlete whose event is the shot put releases a shot. when the shot whose path is shown by the graph to the right is released at an angle of 55°, its height, f(x), in feet, can be modeled by f(x) = -0.02x² + 1.4x + 6.3, where x is the shot’s horizontal distance, in feet, from its point of release. use this model to solve parts (a) through (c) and verify your answers using the graph. (type an integer or decimal rounded to the nearest tenth as needed.) c. from what height was the shot released? feet (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Understand the problem

We need to find the height from which the shot was released. The height function is \( f(x) = -0.02x^2 + 1.4x + 6.3 \), where \( x \) is the horizontal distance. At release, the horizontal distance \( x = 0 \).

Step2: Substitute \( x = 0 \) into the function

Substitute \( x = 0 \) into \( f(x) \):
\( f(0) = -0.02(0)^2 + 1.4(0) + 6.3 \)

Step3: Calculate the value

Simplify the expression:
\( f(0) = 0 + 0 + 6.3 = 6.3 \)

Answer:

6.3