A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent?
t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground
t = 1.5; it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground
t = 3; it takes 3 seconds to reach the maximum height and 3 seconds to fall back to the ground

Question

A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent?
 t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground
 t = 1.5; it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground
 t = 3; it takes 3 seconds to reach the maximum height and 3 seconds to fall back to the ground

Eiwoh2 · Answer

t = 3; it takes 3 seconds to reach the maximum height and 6 seconds to fall back to the ground

joshiscool · Answer

Uhhhhh

Eiwoh2 · Answer

yeah im stuck on this....

Eiwoh2 · Answer

whos good at math? that you know?

Eiwoh2 · Answer

HELP :(

joshiscool · Answer

@YoursTruly @Yinshy @Naruko885 @Ultrilliam

Zepdrix · Answer

Well the axis of symmetry represents the highest point the ball reaches. But all of the options include that, so that doesn't really help us.

Zepdrix · Answer

$$\large\rm h(t) = −16t^2 + 48t$$Factoring out a -16,$$\large\rm h(t)=-16(t^2-3t)$$We will put this parabola into `vertex form`. The x-coordinate of the vertex will be the line of symmetry.

Zepdrix · Answer

|dw:1484080149178:dw|

Zepdrix · Answer

Take half of the b coefficient and square it.
$$\large\rm \left(\frac{-3}{2}\right)^2\quad=\quad 2.25$$

This is the value that will complete the square for us.
Actually I guess we don't need to do that much work...
Putting it into vertex form we know it will looking like this,

$\large\rm h(t)=-16\left(x-1.5\right)^2+stuff$

Where the vertex is located at (1.5, stuff).
We really only care about the x-coordinate of the vertex though.

Zepdrix · Answer

Oh i switched from t's to x's >.< sorry

Zepdrix · Answer

So the ball reaches it's highest point in 1.5 seconds,
and takes a total of 3 seconds to fall to the ground.

Mmmmmm I hope that's not too confusing...

Iamrokmusik · Answer

You want to do two things here.  Take the derivative of the function and factor the function.

-16t(t-3)=h(t) This is factored.  The height ='S zero at t=0 and t=3. Meaning the ball is in the air for a total of 3 seconds.

-32t+48 is the derivative.  Setting this equal to zero and solving for t we get 1.5.  This is the time at which the ball reaches its highest point.  It also means that the ball rises for 1.5 seconds and falls for the same amount of time.

Guessing here cause I'm not sure what you mean.  X=1.5 is the axis of symmetry. And it means that the curve from x=0 to x=1.5 mirrors the curve from x=1.5 to x=3.