To evaluate the function \( h = -6t^2 + 33t + 6 \) at the given values of \( t \) (0, 1, 2, 3, and 4), we’ll compute the height \( h \) for each of these time values.
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For \( t = 0 \): \[ h(0) = -6(0)^2 + 33(0) + 6 = 6 \] So, the point is \( (0, 6) \).
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For \( t = 1 \): \[ h(1) = -6(1)^2 + 33(1) + 6 = -6 + 33 + 6 = 33 \] So, the point is \( (1, 33) \).
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For \( t = 2 \): \[ h(2) = -6(2)^2 + 33(2) + 6 = -24 + 66 + 6 = 48 \] So, the point is \( (2, 48) \).
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For \( t = 3 \): \[ h(3) = -6(3)^2 + 33(3) + 6 = -54 + 99 + 6 = 51 \] So, the point is \( (3, 51) \).
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For \( t = 4 \): \[ h(4) = -6(4)^2 + 33(4) + 6 = -96 + 132 + 6 = 42 \] So, the point is \( (4, 42) \).
Now we can summarize the points we've calculated:
- \( (0, 6) \)
- \( (1, 33) \)
- \( (2, 48) \)
- \( (3, 51) \)
- \( (4, 42) \)
The correct response that matches the corresponding y-values for the x-values of 0, 1, 2, 3, and 4 is: \[ \text{(0,6), (1,33), (2,48), (3,51), and (4,42)} \]
So, the answer is: \[ \text{(0,6), (1,33), (2,48), (3,51), and (4,42)} \]