the function h(t) = -16t2 + 24t models the height, in feet, of a kangaroo t seconds after it jumps. what is…
the function h(t) = -16t2 + 24t models the height, in feet, of a kangaroo t seconds after it jumps. what is the maximum height of the jump?
Answer
Explanation:
Step1: Identify the form of the function
The function $h(t)=-16t^{2}+24t$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 24$, $c = 0$.
Step2: Find the time $t$ at which the maximum occurs
The $t$-coordinate of the vertex of a quadratic function $y=ax^{2}+bx + c$ is given by $t=-\frac{b}{2a}$. Substituting $a=-16$ and $b = 24$ into the formula, we have $t=-\frac{24}{2\times(-16)}=\frac{24}{32}=\frac{3}{4}$.
Step3: Find the maximum height
Substitute $t = \frac{3}{4}$ into the function $h(t)$. So $h(\frac{3}{4})=-16\times(\frac{3}{4})^{2}+24\times\frac{3}{4}=-16\times\frac{9}{16}+18=-9 + 18=9$.
Answer:
9