Answer:
(c) y = -16(x -2)² +68
Step-by-step explanation:
You want the equation that models the table ...
(x, y) = (0, 4), (1, 52), (2, 68), (3, 52), (4, 4).
The table indicates the maximum height is 68 ft at x = 2 seconds. The equation in vertex form will look like ...
y = a(x -h)² +k . . . . . . . . . quadratic with vertex (h, k)
y = a(x -2)² +68 . . . . . . . . quadratic with vertex (2, 68)
We can find the value of 'a' by considering a point where x differs from 2 by 1 unit. (3, 52) is such a point.
52 = a(3 -2)² +68
-16 = a
Then the complete equation of motion is ...
y = -16(x -2)² +68 . . . . . . matches choice C
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Additional comment
This is consistent with the usual ballistic motion equation ...
y = -16x² +v₀x
which has -16 as its leading coefficient.