Explanation:
A) The constant term 125 is the initial height of the stone in meters.
B) The vertex of a parabola y = ax² + bx + c is located at x = -b/(2a).
In this case, b = 12.75 and a = -4.5. The vertex is at:
x = -12.75 / (2 × -4.5)
x ≈ 1.42
This corresponds to a height of:
h = 125 + 12.75 (1.42) − 4.5 (1.42)²
h ≈ 134 m
C) When the stone lands, h = 0.
0 = 125 + 12.75 x − 4.5 x²
Use quadratic formula to solve for x.
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -12.75 ± √(12.75² − 4 (-4.5) (125)) ] / 2(-4.5)
x = (-12.75 ± 49.12) / -9
x ≈ 6.87 m