Answer:
Rocket. B reaches a maximum height that is greater than the maximum height of Rocket A/
Step-by-step 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 [tex]y=ax^2+bx+c[/tex] is: [tex]x_{vertex}=-\frac{b}{2a}[/tex]
therefore, analyzing each rocket trajectory at a time, we get:
Rocket A:
[tex]x_{vertex}=-\frac{96}{(-6)\,2} =8[/tex]
Then we evaluate the rocket's position expression for x = 8:
[tex]y=-6(8)^2+96(8)=384[/tex]
Rocket B:
[tex]x_{vertex}=-\frac{80}{(-4)\,2} =10[/tex]
Then we evaluate the rocket's position expression for x = 10:
[tex]y=-4(10)^2+80(10)=400[/tex]
Therefore, rocket B reaches a greater maximum height than rocket A
