Question

Rocket A; y=-6x^2+96x. Rocket B:y=-4c^2+80x. Rocket. —- reaches a maximum height that is greater than the maximum height of Rocket ——/

Answer 1

Rocket. B reaches a maximum height that is greater than the maximum height of Rocket A/

Explanation:

Notice that both expressions for the rockets' height are parabolas with branches pointing down (they both have a negative leading coefficient), so in order to find the maximum altitude they reach, we just need to find the y-value associated with the vertex of those parabolas.

Recall that the x-value of the parabola's vertex for a parabola of the form
`y=ax^2+bx+c` is:
`x_(vertex)=-(b)/(2a)`

therefore, analyzing each rocket trajectory at a time, we get:

Rocket A:

`x_(vertex)=-(96)/((-6)\,2) =8`

Then we evaluate the rocket's position expression for x = 8:

`y=-6(8)^2+96(8)=384`

Rocket B:

`x_(vertex)=-(80)/((-4)\,2) =10`

Then we evaluate the rocket's position expression for x = 10:

`y=-4(10)^2+80(10)=400`

Therefore, rocket B reaches a greater maximum height than rocket A