Question

medal for best answer :):):)


a toy rocket was launched from the ground. the function f(x)=-16x^2+128x shows the height of the rocket f(x) in feet, from the ground at time x seconds. what it the axis of symmetry of the graph of f(x)and what does it represent?

Answer 1

a.)x=8takes 8 seconds to reach maximum height, 8 seconds to fall back to the ground.
b.)x=4takes 4 seconds to reach maximum height,4 seconds to fall back to the ground.
c.)x=8takes 8 seconds to reach maximum height,16 seconds to fall back to the ground.
d.)x=4 takes 4 seconds to reach maximum height, 8 seconds to fall back to the ground.

Answer 2

@surjithayer

Answer 3

Alright well we see this is an upside down parabola...

lets find the vertex (where it changes direction)

\[\large -\frac{b}{2a} = -\frac{128}{2(-16)} = \frac{128}{32} = 4\] so the 'x' coordinate of our vertex is 4...

so I'm going to say the rocket would take 4 seconds to get up to maximum height...and then it will fall back down taking 4 seconds

How do i know it will only take 4 seconds to get down? Well I would find out the x-intercepts of the parabola by factoring

-16x^2 + 128x = 0
factor our like terms
-16x(x - 8) = 0

so we have 2 equations

-16x = 0
and
(x - 8) = 0

well that means our 2 x intercepts are 0 and 8

So if it take 4 seconds to go up to the max height...we only have 4 seconds to fall back down

Hence the answer being B

Answer 4

thanks :)