Question

jake tosses a coin - up in the air and lets it fall on the ground. the equation that models the height (in feet) and time (in seconds) of the parabola is (h(t)=-16t^{2}+24t + 6). when does the coin reach its greatest height?
15 seconds
1 second
0.75 seconds
0 seconds

Explanation:

Step1: Identify the formula for vertex - time.

For a quadratic function $h(t)=at^{2}+bt + c$, the time $t$ at which the vertex (maximum or minimum) occurs is given by $t=-\frac{b}{2a}$. In the given function $h(t)=-16t^{2}+24t + 6$, $a=-16$ and $b = 24$.

Step2: Calculate the time.

Substitute $a=-16$ and $b = 24$ into the formula $t=-\frac{b}{2a}$. So, $t=-\frac{24}{2\times(-16)}=\frac{24}{32}= 0.75$.

Answer:

0.75 seconds