Main content

## Passport to advanced mathematics

# Interpreting nonlinear expressions — Basic example

## Video transcript

- [Instructor] We're
told the function above models the height h, in meters, of a basketball above ground t seconds after being thrown straight up in the air. What does the number 1.2
represent in the function? So pause this video and
think about it on your own before we work through it together. All right, so we could just
visualize what's happening when you throw a basketball
straight up in the air. This is the ground. Let's say this is the person
throwing the basketball. This is the basketball. It starts at some height. So whatever height this is, that's its initial
height at t equals zero. And then, it's gonna be thrown
with some upward velocity. And it's initially going
to be a high velocity, but then it's gonna slow down. And then, at some point,
it's gonna be stationary, and then it's gonna start
accelerating back downwards. Now, as I mentioned, at t equals zero, what do we see over here? Well, let's see, h of zero is going to be equal
to, this term goes away, 'cause anything times zero is zero. That term goes away. And we're just left with 1.2, the exact number that
they're thinking about. So if you think about it, h of zero, this tells you the position of the ball, in terms of meters above the ground, right when we are starting. So it's telling us the
initial height of the ball. So let's see, it looks like that's exactly what they're saying for choice A, the initial height, in
meters, of the basketball. The maximum height in
meters of the basketball? No, that's definitely not saying that. The maximum height is not going to occur at t equals zero. It's going to occur sometime after that. Rule that one out. The amount of time in seconds the basketball remains airborne. No, that's not the case. Any value that h takes on, remember, h is in meters. T, which is an input into
the function, is time. So if you're talking about
something that h is equal to, which, in this case, h is equal to 1.2 and t is equal to zero, you're talking about a
height above the ground. And then the initial speed. Well, once again, no, this is h of zero, which is the height above the ground. So we like choice A.