Question

Please help me . I need help with this. I’m getting very very frustrated !!! You can get 35 points !

Answer 1

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

$\text{AOS: }x=\dfrac{-b}{2a}\quad \rightarrow \quad x=\dfrac{-(30)}{2(-16)}=\dfrac{-30}{-32}=\dfrac{15}{16}\\\\\\\text{Maximum: }h\bigg(\dfrac{15}{16}\bigg)=-16\bigg(\dfrac{15}{16}\bigg)^2+30\bigg(\dfrac{15}{16}\bigg)+6\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{-225}{16}+\dfrac{450}{16}+\dfrac{96}{16}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{321}{16}\\\\\\.\qquad \qquad \qquad \qquad \approx20.1$

6) h(t)=-16t²+64t+80

$\text{AOS: }x=\dfrac{-b}{2a}\quad \rightarrow \quad x=\dfrac{-(64)}{2(-16)}=\dfrac{-64}{-32}=2$