Answer:
33.7 m at 1.7 seconds
Step-by-step explanation:
For quadratic ax^2+bx+c, the line of symmetry (x-coordinate of the vertex) is ...
-b/(2a)
For your quadratic, the vertex (highest point) is reached at time ...
t = -(17)/(2(-4.9)) = 17/9.8 ≈ 1.7 . . . . seconds
__
The height at that time is ...
f(17/9.8) = (-4.9(17/9.8) +17)(17/9.8) +19 = 289/19.6 +19 ≈ 33.7 . . . meters
_____
Comment on the function evaluation
We have used the "Horner form" of the function to make evaluation easier.
f(t) = (-4.9t +17)t +19
