Question

Consider the function f(x) = -0.01x^2 + 1.18x + 3, where x is the horizontal distance traveled and f(x) is the height of the ball. How far did the ball travel when it reached the maximum height, and how high was the maximum height?

Answer 1

To find the maximum height of the ball, calculate the vertex of the parabola using the formula x = -b/(2a). The horizontal distance at which the maximum height is reached is 59 meters, and you get the maximum height by substituting x = 59 back into the function.

Step-by-step explanation:

The function f(x) = -0.01x^2 + 1.18x + 3 represents the height of a ball over horizontal distance x. To find the maximum height, we need to find the vertex of the parabola. This can be done using the vertex formula for a parabola x = -b/(2a), where a and b are the coefficients from the quadratic equation ax^2 + bx + c.

In this case, a = -0.01 and b = 1.18, so the horizontal distance at which the maximum height is reached is x = -1.18 / (2 * (-0.01)) = 59. Plugging this back into the function gives us the maximum height: f(59) = -0.01(59)^2 + 1.18(59) + 3, which is the height of the ball.

To solve this, simply calculate the value of the function at x = 59. The solution will give you the maximum height the ball reaches, and the x-value is the distance traveled when the maximum height is reached.