I can do each of the things I asked above.
So, let's change this into vertex form:
[tex]h=-16t^2+36t+4[/tex]
[tex]h=(-16t^2+36t)+4[/tex]
[tex]h=-16(t^2-2.25t)+4[/tex]
[tex]h=-16(t^2-2.25t+1.27-1.27)+4[/tex]
[tex]h=-16(t^2-2.25t+1.27)+20.32+4[/tex]
[tex]h=-16(t-1.125)^2+24.32[/tex]
The vertex is at (1.125,24.32)
Answers may vary due to rounding
Factored Form:
[tex]h = -16t^2 + 36t + 4[/tex]
[tex]h = -4\left(4t^2-9t-1\right)[/tex]
Quadratic Formula:
[tex]x = \frac{-b +/- \sqrt{b^2-4(a)(c)}}{2a} [/tex]
h = -16t^2 + 36t + 4
a = -16 b = 36 c = 4
[tex]h = \frac{-(36) +/- \sqrt{(36)^2-4(-16)(4)}}{2(-16)}[/tex]
[tex]h = \frac{-36 +/- \sqrt{1552}}{-32}[/tex]
[tex]h = ≈-0.11 [/tex]
[tex] h = ≈2.36[/tex]
