Question

A football is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t2 + 64t 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?

Answer 1

t = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground

t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground

t = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground

t = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground

Answer 2

Do you know how to solve this? You have \[h(t)=-16t ^{2}+64t\]If this was a "regular" equation and you were told to factor it, what could you factor out of the -16t^2 + 64t? When you do that, you get your answer. But one step at a time. Tell me what the common "thing" is between -16t^2 + 6t and we will go from there.

Answer 3

I have no idea how to do any of it...

Answer 4

Ok, look at it like this\[y = -16x ^{2}+64x\]Can you factor that?

Answer 5

i dunno

Answer 6

You have a 16x in common. You could actually factor out a -16x. When you do that you get y = -16t(t-4). I put the t's back in. I though maybe looking at it with x's in it would put it into a more familiar form, but it doesn't so t will work just as well. h(t) means the height of the function at a certain time. h(t) is our y. Just like f(x) is a y. Get that?

Answer 7

Do you know what this graph looks like?

Answer 8

nope.-.

Answer 9

It is a parabola. When the ball is throw upwards from the ground, it goes up to a certain point, its highest point, then comes back down. Drawn very crudely it looks like this.

Answer 10

Do you know what type of a quadratic that is?

Answer 11

no..

Answer 12

It's a parabola. Are you doing these in school right now?

Answer 13

virtual school...
but i dont learn anything soooo im just about failing right now

Answer 14

Ok, the idea here is to find the highest point on the graph. When you factor out a -16t, you get h(t) = -16t(t-4). In a "regular" equation that you are factoring, you would be solving for t, right? And in order to do that you set each expression on the right side of the equation equal to 0. That would be -16t = 0 and t - 4 = 0. Solve both of these for t. In -16t = 0, dividing both sides by -16 you get t = 0. In t - 4 = 0 you add 4 to both sides giving you t = 4. That means that when the ball comes down after being thrown into the air, it lands at 4 on our x axis. Doesn't do a whole lot for you to help solve the problem but to show you what the graph looks like.