Question

A football throw is modeled by the function h(x) = -0.0065x^2 + 0.5x + 5, where h is the height of the ball in feet and x is the horizontal distance in feet that the ball travels. Find the maximum height of the ball to the nearest tenth of a foot.

a) 10.3 feet
b) 11.2 feet
c) 12.1 feet
d) 13.0 feet"

Answer 1

The maximum height of the football is found by calculating the y-coordinate of the vertex of the quadratic function h(x). By substituting the x-coordinate of the vertex into the function, we determine the maximum height to be approximately 12.1 feet.

Step-by-step explanation:

To find the maximum height of the football to the nearest tenth of a foot, we use the function h(x) = -0.0065x^2 + 0.5x + 5, which models the height (h) of the ball as a function of the horizontal distance (x) it travels. Since this is a quadratic function in the form of ax^2 + bx + c, the x-coordinate of the vertex will give us the horizontal distance at which the ball reaches its maximum height, and the y-coordinate of the vertex will give us the maximum height itself.

The x-coordinate of the vertex can be found using the formula -b/(2a), where a and b are coefficients from the quadratic function. In this case, a = -0.0065 and b = 0.5. Plugging these values into the formula yields x = -0.5 / (2 * -0.0065), which simplifies to x = 38.4615.

Now we substitute x = 38.4615 back into the original equation to find the maximum height:h(38.4615) = -0.0065(38.4615)^2 + 0.5(38.4615) + 5. When we calculate this, we get the maximum height to be approximately 12.1 feet, which corresponds to option (c).