Question 446820
Here's a plot of your equation:
{{{ graph( 400, 400, -100, 100, -100, 100, .0032x^2 + x + 3) }}}
As you can see, it makes no sense at all. The ball just keeps gaining
altitude like a space shot.
I think the equation should be:
{{{ f(x) = -.0032x^2 + x + 3 }}} The first term rpresents the downward pull of gravity
Here's the plot4
{{{ graph( 500, 500, -100, 380, -100, 100,- .0032x^2 + x + 3) }}}
This makes a lot more sense
The ball hits the ground when {{{ f(x) = 0 }}}
{{{ -.0032x^2 + x + 3 = 0 }}} 
Use the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -.0032 }}}
{{{ b = 1 }}}
{{{ c = 3 }}}
{{{x = (-1 +- sqrt( 1 - 4*(-.0032)*3 ))/(2*(-.0032)) }}}
{{{x = (-1 +- sqrt( 1 + .0384 ))/(-.0064) }}}
{{{x = (-1 - 1.019)/(-.0064) }}} (note that only the (-) square root makes sense)
{{{ x = -2.019 / -.0064 }}}
{{{ x = 315.47 }}}
The ball is 315.47 ft from home plate when it lands.
This is confirmed by the graph