Question

adriana jumps off a diving board into a swimming pool. her height above the water changes according to the function h(t)=-16t² + 16t + 15, where t is time in seconds and h(t) is height above the water in feet. according to the function, what is the maximum height that adriana reaches? a. 15 feet b. 15 1/2 feet c. 16 1/2 feet d. 19 feet

Explanation:

Step1: Identify the function type

The function $H(t)=- 16t^{2}+16t + 15$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 16$ and $c = 15$.

Step2: Find the t - value of the vertex

The formula for the $t$ - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is $t=-\frac{b}{2a}$. Substitute $a=-16$ and $b = 16$ into the formula: $t=-\frac{16}{2\times(-16)}=\frac{16}{32}=\frac{1}{2}$.

Step3: Find the maximum height

Substitute $t = \frac{1}{2}$ into the function $H(t)$: $H(\frac{1}{2})=-16\times(\frac{1}{2})^{2}+16\times\frac{1}{2}+15$. First, calculate $-16\times(\frac{1}{2})^{2}=-16\times\frac{1}{4}=-4$. Then, $16\times\frac{1}{2}=8$. So $H(\frac{1}{2})=-4 + 8+15=19$.

Answer:

19 ft