Question

Sam hits a golf ball. The golf ball's height is modeled by the equation below where h(t) is the height in feet and t is the time in seconds after the golf ball is hit. What is the maximum height of the golf ball? Write your answer as a decimal.

Answer 1

Main Answer:

The maximum height of the golf ball can be determined by finding the vertex of the quadratic equation representing the height of the golf ball.

Step-by-step explanation:

1. The equation
`\(h(t)\)` represents the height of the golf ball as a function of time, and it is typically modeled as a quadratic equation of the form
`\(h(t) = at^2 + bt + c\)`.

2. The vertex form of a quadratic equation is given by
`\(h(t) = a(t - h_0)^2 + k_0\)`, where
`\((h_0, k_0)\)` is the vertex.

3. In this form, the maximum height is given by the y-coordinate of the vertex, which is
`\(k_0\)`.

4. To find
`\(k_0\)`, compare the given equation to the vertex form and identify the value of
`\(k_0\)`.

5. The maximum height of the golf ball is then the value of
`\(k_0\)`, and it should be expressed as a decimal.

Therefore, by analyzing the quadratic equation and identifying the vertex, you can determine the maximum height of the golf ball as the y-coordinate of the vertex.