SOLUTION: A football is kicked 70cm from the ground and follows a parabolic path. When it was 4m from where it was kicked, its height was 5.7m and it lands 10m from where it was kicked. Find

Question 1043668: A football is kicked 70cm from the ground and follows a parabolic path. When it was 4m from where it was kicked, its height was 5.7m and it lands 10m from where it was kicked. Find the maximum height reached by the ball, by first forming an equation.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A football is kicked 70cm from the ground and follows a parabolic path.
When it was 4m from where it was kicked, its height was 5.7m and it lands 10m from where it was kicked.
Find the maximum height reached by the ball, by first forming an equation.
:
Change 70cm to .7 meters
:
Using the form ax^2 + bx + c = y
Form three x/y points
0,.7; the point it is kicked (c=.7)
4, 5.7
10, 0; the point where it lands
:
Write an equation for the 2nd and 3rd points
4^2a + 4b + .7 = 5.7
16a + 4b = 5
and
10^2a + 10b + .7 = 0
100a + 10b = -.7
Use elimination, multiply the 1st equation by 10, 2nd equation by 4
160a + 40b = 50
400a + 40b = -2.8
------------------ subtraction eliminates b, find a
-240a = 52.8
a = 52.8/-240
a = -.22
Find b, a=-.22
16(-.22) + 4b = 5
-3.52 + 4b = 5
4b = 5 + 3.52
4b = 8.52
b = 8.52/4
b = 2.13
:
The equation: y = -.22x^2 + 2.13x + .7
:
looks like this

"Find the maximum height reached by the ball"
Find the axis of symmetry, x = -b/(2a)
x =
x = 4.84
Find the max height when x=4.84
y = -.22(4.84^2) + 2.13(4.84) + .7
y = -5.155 + 10.31 + .7
y = 5.8556 meters max height (green line)

RELATED QUESTIONS
When a ball is thrown or kicked, the path it travels is shaped like a parabola. Suppose a (answered by Alan3354,greenestamps)

from the center of the 20yd (60ft) line, a football player attempts to make a field goal... (answered by Edwin McCravy)

from the center of the 20yd (60ft) line, a football player attempts to make a field goal... (answered by ankor@dixie-net.com)

Please help me solve this question When a ball is thrown or kicked, the path it... (answered by ikleyn)

A football initially on the found is kicked in the air and follows a parabolic path... (answered by jsmallt9)

A football is kicked in the air and lands on the ground 32m from where it was kicked. If... (answered by jrfrunner)

A football initially on the ground is kicked in the air and follows a parabolic path... (answered by ankor@dixie-net.com)

Sarah and Tom kicked a soccer ball from ground level. For Sarah it travelled 31m... (answered by stanbon)

A football is kicked straight up into the air; it hits the ground 3.6s later.What was the (answered by josmiceli)