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

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

6) h(t)=-16t²+64t+80

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