Answer
The line of symmetry is at $x=3.75$. This means that the graph is reflexive over this line. For any point on the right hand side of the graph with a given $y$ value, there is another point $x$ that has the same $y$ value.
Example: For $x=.4$ and $x=7.1$, both points have a y-value of 350.
That is why part (a) has two answers.
Work Step by Step
$h(t) =-16t^2+120t+300$
$x=-16$, $b=120$, $c=300$
$x=-b/2a$
$x=-120/2*-16$
$x=-120/-32$
$x=60/16$
$x=30/8$
$x=15/4$
$x=3.75$
Line of symmetry is at $x=3.75$
$h(t)=350$
$350=-16t^2+120t+300$
$350-350=-16t^2+120t+300-350$
$0=-16t^2+120t-50$
$0=(-16t^2+120t-50)/2$
$0=-8t^2+60t-25$
$a=-8$, $b=60$, $c=-25$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-60±\sqrt {60^2-4*(-8)*-25})/2*-8$
$x=(-60±\sqrt {3600-800})/-16$
$x=(-60±\sqrt {2800})/-16$
$x=(-60±\sqrt {4*7*100})/-16$
$x=(-60±20\sqrt 7)/-16$
$x=(-60±20*2.645)/-16$
$x=(-60±52.915)/-16$
$x=(-60+52.915)/-16$
$x=-7.085/-16$
$x=.4428$
$x=.4$
$x=(-60-52.915)/-16$
$x=-112.915/-16$
$x=7.05625$
$x=7.1$
