Question 56231
The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, {{{y=-0.042x^2+5x}}}, where x is the distance in yards from the point it was hite and y is the height of the golf ball in feet. Assume that the ground is level.
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a. Find the maximum height reached by the ball.
The y value of the vertex is the maximum height the ball.  We can find the x value of the vertex with the formula:{{{highlight(x=-b/2a)}}}.  The b and a we get from the standard form of a parabola: {{{y=ax^2+bx+c}}}.  Our a=-0.042 and out b=5.
{{{x=-(5)/(2(-0.042))=59.5238}}}
Subtstitute that value into {{{y=-0.042x^2+5x}}} to find the maximum height.
{{{y=-0.042(59.5238)^2+5(59.5238)}}}
Plug that into your calculator and you'll find the maximum height to be {{{highlight(y=148.81ft)}}}.
:
b. How far from where it was hit does the ball hit the ground?
The x-intercepts represent the position of the ball.  Let y=0, factor and solve for x.
{{{0=-0.042x^2+5x}}}
{{{0=x(-0.42x+5)}}}
x=0 is the starting position. 
-0.42x+5=0
-0.42x=-5
-0.42x/-0.42=-5/-0.42
{{{highlight(x=199.05ft)}}} is where it lands.
Happy Calculating!!!