In high school, I played soft ball. I hit the ball into the air with an upward velocity of 35 ft. The equation that gives the height (h) of the ball at any time (t) is: h(t)= -15t2 + 35ft + 1.0. What is the y-coordinate of the vertex?

Use: x=-b/2a

correction:

on this good earth of ours the equation would be
h(t) = -16t^2 + 35t + 1
I assume you had a typo.

the t of the vertex (instead of the normal x)
= -b/2a = -35/-32

so h(35/32) = -16(35/32)^2 + 35(35/2) + 1
= appr 20.14

(exact answer is 1289/64)