Question 144379
Given: {{{h=-16t^2+39t+100}}}    you missed the t^2 

To plot the graph, you realize that since the equation is quadratic, the shape is a parabola. You are asked to find two points. I think you need to plot 4 points to draw a 'good graph' for this one.

Point 1 is the starting point. You are told that at time=0, the height is 100. (0,100)

Now find these three other points.
Find the other point where the height is 100. The projectile goes up, so it will come down.

To find that other point, replace h with 100 and solve
{{{100=-16t^2+39t+100}}}
{{{0=t (-16t+39)}}}
t = 0, t= 39/16   (you see that point 1 is one of these. Point 3 the other one
(39/16, 100)

Now find the point at the time halfway between points 1 and 3. That time is 
{{{(1/2)(39/16)}}} = {{{39/32}}}. Plug that in for t and see what h is. Use that as point 2


The last point is the poiint where the projectile hits the ground. At that point, h =0.
{{{0 =-16t^2+39t+100}}}
Use the quadratic equation with a=(-16), b=39 and c=100 to find the positive time. Plot that as point 4 (t,0).

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

Now draw the curve.