Question 962512
{{{ h(t) = -10.5 t^2 + 66.3t + 6 }}}
The {{{ t }}} component of the max height is
found with the formula:
{{{ t[max] = -b/(2a) }}}
where the quadratic has the general form:
{{{ y = ax^2 + b*x + c }}}
You've got {{{ h(t) }}} instead of {{{ y(x) }}}
{{{ a = -10.5 }}}
{{{ b = 66.3 }}}
{{{ t[max] = -66.3/(2*(-10.5)) }}}
{{{ t[max] = -66.3 / ( -21 ) }}}
{{{ t[max] = 3.16 }}} sec
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Now find {{{ h(t) = h( 3.16 ) }}}
{{{ h(t) = -10.5 *3.16^2 + 66.3*3.16 + 6 }}}
You can finish
Here's the plot:
{{{ graph( 400, 400, -2, 10, -10, 120, -10.5x^2 + 66.3x + 6 ) }}}