This is more of a physics question unless you were given an equation for height vs time in english units (math texts often still use y = y0 + v0t - 16t2 (v0 is the velocity at t=0, y0 is the height at t = 0, and y and t are height and time respectively).
To find the time to the peak you can look at the upside-down parabola y = 35 + 192t - 16t2 and find it's apex which will be the max y value. This is beyond algebra 1, but it is doable in several ways. You can complete the square and put the parabola into vertex form which will pinpoint the vertex. Also, with calculus, you can solve for the 0 in velocity (1st derivative) and find t so that 192 - 32tpk = 0 This will find the time to the peak and you can plug into the equation for y to find ypk
JACQUES D.
07/05/22
Robert K.
I take no issue with the accuracy of your equation but I disagree with your statement that finding the vertex of a parabola is beyond Algebra 1. Students are taught that the x coordinate of the vertex is -b/2a. (They are not told that it comes from setting the first derivative equal to zero. They don know, or need to know, what a first derivative even is.) Then they are taught to put that value of x, in this case t, into the equation to get y, in this case h.They also know that a negative a means the parabola opens downward and therefore has a maximum.07/05/22