Question 831047
If the graph is drawn out, it shows the trajectory of the basketball if it were to be shot by Azim.

The goal is to find the y value of the vertex in the equation, which will be the maximum height that the ball reaches.

 Remember that the {{{-(t^2)}}} part in the function is negative so the parabola is pointing downwards. Negative parabolas have maximums which is the vertex.

The expression for the vertex of a parabola is {{{x = (-b)/(2*a) }}}.
So if you plug in the numbers corresponding to the equation it should look like this

{{{(-(4))/(2*-1) }}} This should give you an answer of 2. Now, the expression for vertex is an equation for the x value of the vertex.
So, you need to find the y value. You do this by plugging 2 into the equation
{{{h(t)=-t^2+4t+6, h(t)}}} which would look like this
{{{-(2)^2+(4*2)+6}}}

Which gives you a y value of 10. The basketball will reach a maximum height of 10 feet.