Respuesta :
You have the following quadratic function to determine the height of a projectile in time:
[tex]h(t)=-16t^2+544t[/tex]a) The maximum height is given by the y-coordinate of the vertex of the parabola (which is the representation of the given quadratic function).
Take into account that in general, a quadratic function can be written as follow:
[tex]at^2+bt+c[/tex]where a, b and c are coefficients.
The vertex of the function is given by:
[tex]t=-\frac{b}{2a}[/tex]By comparing with the given function for h, you have a=-16, b=544. Replace these values into the previous formula for t:
[tex]t=-\frac{544}{2(-16)}=\frac{544}{32}=17[/tex]Now, replace the previous value to find h(17):
[tex]\begin{gathered} h(17)=-16(17)^2+544(17) \\ h(17)=4624 \end{gathered}[/tex]Hence, the maximum height reached by the projectile is 4624 feet.
b) The time at which the projectile reaches the maximum is just the value of t in the vertex of the parabola.
Hence, the time the projectile takes to reach the maximum is 17 seconds.
