Question

A rock is thrown into the air, and its height (h) in feet after (t) seconds can be calculated by h(x)=-16t²+18t+1. Estimate the rock's maximum height (round to 2 decimals). Hint: You'll need to find when the rock reaches its maximum height first.

Answer 1

The maximum height of the rock can be estimated by finding the vertex of the quadratic function representing its height. The maximum height of the rock is approximately 0.56 feet.

Step-by-step explanation:

The maximum height of the rock can be estimated by finding the vertex of the quadratic function representing its height. The vertex of a quadratic function in the form f(x) = ax² + bx + c is given by the point (h, k), where h = -b/2a and k is the maximum value of the function. In this case, the function representing the height of the rock is h(t) = -16t² + 18t + 1. So, we can find the vertex by using the formula h = -b/2a. Substituting the values for a and b from the function, we get h = -(18)/(2(-16)) = 9/16. Therefore, the rock's maximum height is approximately 0.56 feet.