Notes:
- The sign of the coefficient of the quadratic equation determines if the vertex is a minimum or maximum. Positive looks like ∪ so has a minimum. Negative looks like ∩ so has a maximum.
- Maximum/minimum height is the y-value of the vertex.
- Time to reach maximum height is the x-value of the vertex (which is also the Axis-Of-Symmetry).
Answer: 4) maximum
5) 20.1 ft
6) 2 seconds
Step-by-step explanation:
4) h(t) = -16t² + 256t
↓
the coefficient is negative so it looks like ∩.
Therefore, it has a maximum.
5) h(t) = -16t² + 30t + 6
[tex]\text{AOS: }x=\dfrac{-b}{2a}\quad \rightarrow \quad x=\dfrac{-(30)}{2(-16)}=\dfrac{-30}{-32}=\dfrac{15}{16}\\\\\\\text{Maximum: }h\bigg(\dfrac{15}{16}\bigg)=-16\bigg(\dfrac{15}{16}\bigg)^2+30\bigg(\dfrac{15}{16}\bigg)+6\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{-225}{16}+\dfrac{450}{16}+\dfrac{96}{16}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{321}{16}\\\\\\.\qquad \qquad \qquad \qquad \approx20.1[/tex]
6) h(t)=-16t²+64t+80
[tex]\text{AOS: }x=\dfrac{-b}{2a}\quad \rightarrow \quad x=\dfrac{-(64)}{2(-16)}=\dfrac{-64}{-32}=2[/tex]
