SOLUTION: Sarah and Tom kicked a soccer ball from ground level. For Sarah it travelled 31m horizontally, it reaches it maximum height of 25m. The soccer ball lands on the ground 62m from whe

Question 918710: Sarah and Tom kicked a soccer ball from ground level. For Sarah it travelled 31m horizontally, it reaches it maximum height of 25m. The soccer ball lands on the ground 62m from where it was kicked. And Tom kicked it 40m horizontally; it reaches the height of 20m. The soccer ball lands on the ground 70m from where it was kicked.
a) Put this in a graph
b) Model the situation with a relation in the form y=a(x-h)^2+k
c) what is the soccer ball's height when it is 50 m from where it was kicked?

HOW DO I ANSWER THIS?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sarah and Tom kicked a soccer ball from ground level. For Sarah it travelled 31m horizontally, it reaches it maximum height of 25m. The soccer ball lands on the ground 62m from where it was kicked.
Draw a parabola that starts at the ground at (0,0) and reaches
the ground at (62,0), and has a maximum point at (x,25)
Note: Because of symmetry, x = 31
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Equation::
y = a(x)(x-62)
Substitute using (31,25) to solve for "a":
25 = a(31)(31-62)
25 = a*(-961)
a = -25/961
y = (-25/961)x(x-62)
y = (-25/961)(x^2-62x + 961)-961(-25/961)
y = (-25/961)(x-31)^2+25
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Height when x = 50::
y = (-25/961(19)^2+25 = 24.5 ft
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And Tom kicked it 40m horizontally; it reaches the height of 20m. The soccer ball lands on the ground 70m from where it was kicked.
a) Put this in a graph
b) Model the situation with a relation in the form y=a(x-h)^2+k
c) what is the soccer ball's height when it is 50 m from where it was kicked?
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The work for Tom's ball is the same as the work for the girl.
Cheers,
Stan H.
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