To calculate the height \( h \) of the volleyball at different times \( t \) using the function \( h(t) = -6t^2 + 33t + 6 \), we'll substitute the values of \( t \) into the function.
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For \( t = 0 \): \[ h(0) = -6(0)^2 + 33(0) + 6 = 6 \]
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For \( t = 2 \): \[ h(2) = -6(2)^2 + 33(2) + 6 \] \[ = -6(4) + 66 + 6 \] \[ = -24 + 66 + 6 = 48 \]
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For \( t = 4 \): \[ h(4) = -6(4)^2 + 33(4) + 6 \] \[ = -6(16) + 132 + 6 \] \[ = -96 + 132 + 6 = 42 \]
Now, we can fill in the table:
\[ \begin{array}{|c|c|} \hline x & h(x) \ \hline 0 & 6 \ 2 & 48 \ 4 & 42 \ \hline \end{array} \]
So the values are:
- \( h(0) = 6 \)
- \( h(2) = 48 \)
- \( h(4) = 42 \)