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Jamie kicked a soccer ball that traveled along a path described by the parabola y = -x^2 +8x, where y equals the height of the soccer ball in feet, and x = the horizontal distance in feet that the ball has traveled from Jamie.  How many feet from Jamie does the soccer ball hit the ground?

2 Answers

5 votes
the answer is 8 feet
User Jessikwa
by
7.3k points
5 votes

Equation of any Parabola is of the form y=
ax^(2)+bx+c

If a is negative the parabola opens down.

The given equation of soccer ball that traveled along a path was y=
-x^(2)+8x

Comparing the two equations we have a=-1,b=8

As a is negative the parabola opens down and will have the maximum point at vertex .

The x of vertex is given by x=
(-b)/(2a)

Substituting a and b values we have:

x=
-(-8)/(2x1) =(8)/(2)= 4.

The y of vertex is y=
(-4)^(2)+8(4) =16

The highest point the soccer ball hit the ground is 16 ft.

User Tiara
by
7.5k points
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