Justin and elena each launched a toy rocket into the air. the height of justin’s rocket is modeled by the equation h = –16t2 + 60t + 2. elena launched his rocket from the same position, but with an initial velocity double that of justin’s. which equation best models the height of elena’s rocket? h(t) = at2 + vt + h0 h = –16t2 + 60t + 4 h = –32t2 + 120t + 4 h = –32t2 + 60t + 2 h = –16t2 + 120t + 2

Step-by-step explanation:

we know that

The height of Justin’s rocket is modeled by the equation

This is the equation of a vertical parabola open downward

The vertex is a maximum

where

The coefficient of t^2 represent the acceleration

The coefficient of t represent the initial velocity

The constant of the equation represent  the initial height

Remember that

Elena launched his rocket from the same position, but with an initial velocity double that of Justin’s

so

Now the initial velocity is

substitute

The height of Elena’s rocket is the equation

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is