Question 735418
A child throws a ball upward from the roof of a house.
 The trajectory is parabolic, according to the laws of physics.
 The height the of the ball above the ground, y in meters is given by the quadratic relation y=-3x^2+6x+4
:
a) How high is the roof of the house where the ball is thrown.
The ball was thrown when x = 0, therefore the roof is 4 meters high
:
b)Complete the square to solve the quadratic equation for the exact values of x when y=0
-3x^2 + 6x + ___ = -4
Coefficient of x has to be 1, divide equation by -3
x^2 - 2x + ___ = {{{4/3}}}
Find the value that completes the square, divide the coefficient of x
 and square it, add to both sides
x^2 - 2x + 1 = {{{4/3}}} + 1
{{{(x-1)^2}}} = {{{7/3}}}
Find the square root of both sides
x - 1 = +/-{{{sqrt(7/3)}}}
Two solutions
x = 1 + {{{sqrt(7/3)}}} ~ 2.53 
and
x = 1 - {{{sqrt(7/3)}}} ~ -.53
:
c) Use the quadratic formula to confirm your answers from part b)
 {{{x = (-6 +- sqrt(6^2-4*-3*4 ))/(2*-3) }}}
You can do the math on this
: 
d) Exactly how far away from the house(horizontally) does the ball hit the ground?
Solution 1 above  x ~ 2.53 meters
:
e) Use your answers from parts b) and c) and determine the horizontal distance from the house when the ball reaches maximum height.
That occurs at the axis of symmetry. x = -b/(2a) is the formula for that
x = -6/(2*-3)
x = 1 meter horizontally from the house it will be max height
:
f) What is the maximum height of the ball?
y = -3(1^2) + 6(1) + 4
y = 7 meters max height