Question 1066433
The equation would be:
{{{ h(t) = -16t^2 + 160t + 70 }}}
This is a parabola with a peak ( not a dip )
The formula for the x-value of the peak is
{{{ x[p] = -b/(2a) }}}
{{{ x[p] = -160/( 2*(-16) ) }}}
{{{ x[p] = 160/32 }}}
{{{ x[p] = 5 }}}
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Plug this value back into equation to get {{{ h[p] }}}
{{{ h[p] = -16*5^2 + 160*5 + 70 }}}
{{{ h[p] = -16*25 + 800 + 70 }}}
{{{ h[p] = -400 + 800 + 70 }}}
{{{ h[p] = 470 }}}
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The maximum height is 470 ft
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check:
Here's the plot:
{{{ graph( 500, 500, -2, 12, -60, 600, -16x^2 + 160x + 70 ) }}}