Answer:
Time: 2/5 or .4
Step-by-step explanation:
Without calculus you can solve this by converting the equation into vertex form.
You can convert to vertex form by completing the square.
[tex]y=24+4t-5t^{2} \\y-24=-5t^{2} +4t\\y-25= -5(t^{2} -\frac{4}{5}) \\y=-5(t-\frac{2}{5} )^{2} +\frac{124}{5}[/tex]
The vertex form is
[tex]y=-5(t-\frac{2}{5} )^{2} +\frac{124}{5}[/tex]
From vertex form we know (h,k) is (2/4,124/5) so the height at the max time is 2/5, and the height is 124/5
