Answer:
After 2 seconds the object reach its maximum height of 80 feet.
Step-by-step explanation:
Consider the provided function.
[tex]f(t)=-16t^2+64t+16[/tex]
The function is a downward parabola.
The object will reach its max height at the vertex of the parabola.
The vertex of the parabola is given by [tex](\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex],
Where the standard form is [tex]f=at^2+bt+c[/tex].
By comparing the provided function with the standard form.
a=-16, b=64 and c=16
Thus, the vertex are:
[tex]t=\frac{-b}{2a}[/tex]
[tex]t=\frac{-64}{2(-16)}=\frac{64}{32}[/tex]
[tex]t=2[/tex]
Now substitute the value of t in the provided function.
[tex]f(t)=-16(2)^2+64(2)+16[/tex]
[tex]f(t)=-16(4)+128+16[/tex]
[tex]f(t)=-64+144[/tex]
[tex]f(t)=80[/tex]
Hence, after 2 seconds the object reach its maximum height of 80 feet.
Answer:
2 seconds
Step-by-step explanation:
When the object reaches its highest point is the t-value of the turning point. Thus we need to find the where maximum quadratic function
−16t2+64t+16
occurs.
We know that the maximum (or minimum) of a parabola is reached at x=−b2a=−642(−16)=2, showing that the object will reach its highest point at 2 seconds.
