Answer:
Range is 0 ≤ h ≤ 32
Step-by-step explanation:
The height is a function of time and is described as h(t) = -8t² + 32t
h is the y-axis and t is the x axis, so we can write this as y = -8x² + 32 x.
This describes a parabola that opens downward, since the coefficient of the square term is negative. The maximum point for height will be at the vertex of the parabola.
y = ax² + bx + c
The x coordinate of the vertex is at -b/2a
a = -8, b = 32, c = 0
-b/2a = -32/-16 = 2
Maximum height is at x = 2 seconds (we can see this on the graph)
At 2 seconds, y = -8(2²) + 32(2) = -32 + 64 = 32
Again, we can see this on the graph.
The x intercepts are the points where y = 0
0 = -8x² + 32x = 8x(-x +4)
y will be 0 when x is 0 or 4 (confirmed by graph)
So, the height (y) = 0 at time (x) = 0 sec, 4 sec
0 ≤ y ≤ 32
y = h, so 0 ≤ h ≤ 32
I hope this helps.
