Solving Problems With Graphs

Prompt: If given the following points in no particular order: (-4, 16), (0,0), (4,16), (1,1), (3,9), (-2,4), (2,4), find any y-values that may exist corresponding with x = -1 and -3.

We can first plot the points given above and draw a line through them.

So for this, I would recommend checking out the , since they do a really good job of easing you into a subject.

The only bad news is that Graph Theory doesn’t pop up until Chapter 2, so you’ll have to knock out the Chapter 1 problems first, and it takes a decent amount of time (although maybe not for you, since you’ve been doing CP for 6 months).

The solution to the system will be in the point where the two lines intersect.

When I was first introduced to Competitive Programming, I avoided graph problems like the plague because I never really understood how to do them, and even when I did, I could never implement the solutions (a terrible mindset to have, mind you).

Finally, graphing can help us solve a couple of real-world problems.

Not to worry, though, there are resources that can help you.

In the very least, we might see if the line drawn through these points corresponds with any familiar functions.

At first glance, the graph above appears to be of a parabolic function.

Can we find a graphical representation of gallons lost to the leak from the basin over time?

Can we determine how long it will take before the basin is halfway empty?

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