A ball is thrown into the air. Its height h, in feet, after x seconds is given by t...
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Problem
A ball is thrown into the air. Its height h, in feet, after x seconds is given by the function h(x) = -16(x - 1)^2 + 23. Part A: What is the vertex of the function? Part B: What does the vertex indicate about the ball?
Step-by-step solution
The function is in vertex form $h(x) = a(x-h)^2 + k$, where the vertex is $(h, k)$. For $h(x) = -16(x - 1)^2 + 23$, the vertex is $(1, 23)$. This means at $x=1$ second, the height $h=23$ feet, which is the maximum height.
Answer
The vertex is (1, 23). This indicates that after 1 second, the ball reaches its maximum height of 23 feet.