Respuesta :
Answer:
Vertex form: [tex]h(t)=-16(t-3)^2+148[/tex]
Height expressed as a function of time: [tex]h(t)=-16t^2+96t+4[/tex]
Step-by-step explanation:
We have been given that the ball is 4 ft above the ground when she hits it.
This means that initial value (y-intercept) of ball is 4.
We are also told that three seconds later it reaches its maximum height of 148 ft. This means [tex]h(3)=148[/tex].
We know that vertex form of a parabola is in format [tex]y=a(x-h)^2+k[/tex].
Let us solve for a using our given information.
[tex]4=a(0-3)^2+148[/tex]
[tex]4=a(-3)^2+148[/tex]
[tex]4=a*9+148[/tex]
[tex]4-148=9a+148-148[/tex]
[tex]-144=9a[/tex]
[tex]a=\frac{-144}{9}[/tex]
[tex]a=-16[/tex]
Therefore, the vertex form of our given function would be [tex]y=-16(x-3)^2+148[/tex].
Since we need height as a function of time, so we will get:
[tex]h(t)=-16(t-3)^2+148[/tex]
[tex]h(t)=-16(t^2-6t+9)+148[/tex]
[tex]h(t)=-16t^2+96t-144+148[/tex]
[tex]h(t)=-16t^2+96t+4[/tex]
Therefore, the function where height is expressed as a function of time would be [tex]h(t)=-16t^2+96t+4[/tex].
