Aball is thrown from an initial height of 7 feet with an initial upward velocity of 33 ft/s. the ball’s height h (in feet) after t seconds is given by the following. h=7+33t-16t^2. find all values of t for which the ball’s height is 23 feet.

Given that the height of the ball has been modeled by:
h(t)=-16t^2+33t+7
the values of t for which h(t)=23 will be evaluated as follows:
from our function, let h(t)=23 hence we shall have:
23=-16t^2+33t+7
re-writing the above we get:
-16t^2+33t-16=0
solving the above using quadratic formula:
t=[-b+/-sqrt(b^2-4ac)]/2a
a=-16, b=33, c=-16
thus
t=[-33+/-sqrt(33^2-4(-16)(-16))]/(-16*2)
simplifying the above we get:
t=33/32+/-sqrt(65)/32
hence
t=1.2832 or 0.779