Jake tosses a coin in the air and lets it fall on the ground. the equation that models the height (in feet) and time (in secounds) of the parabola is h(t)=-26t^2+24t+6. what is the height of the coin when jake tosses it
Answers
Answer:
Answer:
The coin will reach the maximum height of 15 feet in \frac{3}{4}
4
3
second
Step-by-step explanation:
The equation that models the height (in feet) and time in seconds) of the parabola is
h(t)=-16t^2 + 24t + 6h(t)=−16t
2
+24t+6
The coin will reach its greatest height at the parabola's vertex. Find the coordinates of the vertex.
From the function expression:
\begin{lgathered}a=-16\\ \\b=24\\ \\c=6\end{lgathered}
a=−16
b=24
c=6
Now,
\begin{lgathered}t_v=\dfrac{-b}{2a}\\ \\=-\dfrac{24}{2\cdot (-16)}\\ \\=\dfrac{24}{32}\\ \\=\dfrac{3}{4}\ second\end{lgathered}
t
v
=
2a
−b
=−
2⋅(−16)
24
=
32
24
=
4
3
second
Then
\begin{lgathered}h_v=h(t_v)\\ \\=-16\cdot \left(\dfrac{3}{4}\right)^2+24\cdot \dfrac{3}{4}+6\\ \\=-16\cdot \dfrac{9}{16}+18+6\\ \\=-9+24\\ \\=15\ feet\end{lgathered}
h
v
=h(t
v
)
=−16⋅(
4
3
)
2
+24⋅
4
3
+6
=−16⋅
16
9
+18+6
=−9+24
=15 feet