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