make (0,0) the original position, rather than (0, 5.4)
the (20, 15) point then becomes (20, 15-5.4) = (20, 9.6)
and (120, 15) becomes (20, 9.6)
another point on the parabola is (140,0)
zeroes are x= 0 and x = 140
then the parabola is h(x) = (x-0)(x-140) = x^2 - 140x
h(x) = -x^2 +140x is the formula for the height as a function of horizontal distance x
take the derivative and set equal to zero, h'(x) = -2x +140 = 0, x = 70 is when the height is at a maximum. -(70)^2 +140(70) = -4900-9800 = 4900 feet = max height
h(20) = -(20)^2 + 140(20) = -400+2800 = 2400
h(120) = -(120)^2 + 140(120) = -14400 + 16800 = 2400
h(140) = -(140)^2 + 140(140) = 0
h(0) = -0^2 + 140(0) = 0
h(x) = -x^2 + 140x is the parabola which can also be rewritten in vertex form
h(x) = -(x^2 -140x + 4900) + 4900
h(x) = -(x-70)^2 + 4900 is in vertex form where the vertex and maximum point is (70,4900) The maximum height is 4900 feet.
the negative sign indicates the parabola is downward opening
what's confusing about this problem is that deceleration due to gravity would make the coefficient of the x^2 be -16, as the effect of gravity at sea level. At high levels in the mountains a lesser absolute value, but unlikely to be near 1, unless you're up in the stratosphere near where you begin to escape the earth's gravity. Try to use -16 and it's inconsistent with the other numbers in this problem. 5.4 feet above sea level doesn't come close to gravity reduced to -1 feet per second per second. So, the problems is not realistic.And confuses anyone familiar with physics.
