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Sarah_Marie · Oct 18, 2010, 02:18 PM

a soccer ball is kicked from the ground. After travellinga horizontal distance of 35 m, it just passes over a 1.5 m tall fence before hitting the ground 37 m from where it was kicked.

a) Considering the ground to be the x-axis and the vertex to be on the y-axis, determine the equation of a quadratic function that can be used to model the parabolic path of the ball.

b) Determine the maximum height of the ball.

c) How far has the ball travelled horizontally to reach the maximum height?

d) Develop a new equation for the quadratic function that represents the height of the ball, considering the badd to have been kicked from the origin.

galactus · Oct 19, 2010, 02:20 AM

Originally Posted by Sarah_Marie

a soccer ball is kicked from the ground. After travellinga horizontal distance of 35 m, it just passes over a 1.5 m tall fence before hitting the ground 37 m from where it was kicked.

a) Considering the ground to be the x-axis and the vertex to be on the y-axis, determine the equation of a quadratic function that can be used to model the parabolic path of the ball.

The intercept form of a quadratic is $y=a(x-p)(x+q)$ .

Where p and q are the x-intercepts. In this case, the x intercepts are at

x=-37/2 and x=37/2.

Plug in the given point at the fence, (33/2,3/2), for x and y and solve for a.

$\frac{3}{2}=a(\frac{33}{2}-\frac{37}{2})(\frac{33}{2}+\frac{37}{2})$

This will give the equation of the parabola that models the flight of the ball.

$a(x-\frac{37}{2})(x+\frac{37}{2})$

b) Determine the maximum height of the ball.

Sub in x=0 or just note the constant in your newly found equation.

Sarah_Marie · Oct 20, 2010, 07:56 AM

thank you, so why are the x coordinates over 2?

Unknown008 · Oct 20, 2010, 09:41 AM

The x coordinates are not over two, they are $\frac{37}{2}$ which can also be written as 18.5.