Interpreting key features of polynomial graph applications
About this video
A grasshopper hops between two leaves of equal height, and a graph of g models its height above the first leaf (in cm) against time (in tenths of a second). The video interprets the point (3, 7) as the grasshopper being 7 cm up after 3/10 of a second, which is its peak height, and stresses that the horizontal axis is time, not distance.
You'll be able to
- interpret a point on a graph in context using the units of both axes.
- identify the maximum of a graph and explain what it means in a real situation.
- explain why a time axis tells us nothing about horizontal distance travelled.
Key words
- Input (x)
- The value on the horizontal axis; here, time measured in tenths of a second.
- Output g(x)
- The value on the vertical axis; here, the grasshopper's height above the first leaf in centimetres.
- Peak (maximum)
- The highest point on a graph; here, the greatest height the grasshopper reaches.
Transcript
- [Instructor] We're told a grasshopper is on a milkweed plant. It hops from one leaf to another that has the same height. So if this is one leaf here, there's another leaf over here. This is the same height. I probably should have done that in some type of green color.
And then we have a grasshopper. This is the grasshopper right over here. And the grasshopper jumps from one leaf to the other. Here is a graph of the function g, that models the grasshopper's height from the first leaf in centimeters, g(x) in time, from the first leaf in centimeters, g(x), so the height is in centimeters, over time in tenths of a second.
So this is tenths of a second. Identify the meaning of the point 3, 7. So pause this video, think about it, and then we'll think about it together. All right, so 3, 7 means after 3/10 of a second. So after 3/10 of a second, I could write it like this, 3/10 of a second, this is telling us that the grasshopper is seven...
It tells us that it's in centimeters, the y-axis. So after 3/10 of a second, the grasshopper, I'll use gh for sort, is seven centimeters in the air. And it looks like that's the peak height that the grasshopper actually achieves. So in this drawing right over here, this height right over there is, so if we call these two leaves even, it's gonna be seven centimeters above either of the leaf.
Now, it's important to keep in mind that this axis right over here is time, it's not distance. So we actually don't know how far apart these leaves are. All we know is it took a little under 6/10 of a second for the grasshopper to get from here to here. But we know what the height was at any time.
And that maximum height was seven centimeters or at least seven centimeters above either of the leaves 'cause they're at the same height.
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