Interpret a quadratic graph | Quadratic functions & equations | Algebra 1 | Khan Academy

Katie throws a ball in the air for her dog to chase. The function f models the height of the ball in meters as a function of time in seconds after Katie threw it. We could see that right over here this is our function f.

So at time t equals zero, the height looks like it's a couple of meters. Then, as we go forward in time to a little under two and a half seconds, the ball is going up. After a little under two and a half seconds, the ball starts going down. By the time you get to five seconds, or close to five seconds, it looks like the ball is on the ground; its height is zero meters.

Then they ask us which of these statements are true; choose all that apply. So pause this video and see if you can work it out.

All right, now let's look through the choices. The first one says Katie threw the ball from a height of five meters. So let's see if that bears fruit or if that is true. If she threw it from a height of five meters, that means that the y-intercept would have been at five meters. At time t equals zero, it would have been at a height of five meters. Clearly, that is not the y-intercept; it looks like she threw it from a height of maybe one and a half or two meters.

So I'm assuming that Katie is not five meters tall; she wasn't on a ladder or anything. She just threw it from her regular height, and so we can rule out this first choice.

The second one says at its highest point, the ball was about 31 meters above the ground. Let's see if that is true. So the highest point is right over here, and yeah, that looks about 31 meters. So I like that choice, so I will select that one.

The ball was in the air for about two and a half seconds. So we can clearly see that that is not the case. The ball was going up for about two and a half seconds, but then it was going down for roughly another two and a half seconds. So it was actually in the air for almost five seconds, so I would rule this one out.

The ball reached its highest point in the air about two and a half seconds after Katie threw it. So let's see. After Katie threw it, two and a half seconds after she threw the ball, it's right over there. It looks like it reached its highest point a little bit before that, but they said "about," so they're speaking in rough terms.

I think that statement can be true; it's about two and a half seconds. If they said exactly two and a half seconds, I wouldn't have selected it because it seems like it happened at like 2.45 seconds or something like that. But there you go; those are the ones that seem true.