Solubility | CK-12 Foundation - Free Printable

Let’s solve this step by step.

We are given a graph with several colored lines, each labeled with an equation (like y = 2x + 1, etc.). The task is to find which line corresponds to the equation y = x² - 4.

First, let’s understand what kind of graph y = x² - 4 makes.

This is a quadratic equation, so its graph is a parabola — it looks like a U-shape or an upside-down U. Since the coefficient of x² is positive (+1), it opens upward.

Also, we can find key points on this parabola:

- When x = 0 → y = 0² - 4 = -4 → point (0, -4)
- When x = 2 → y = 4 - 4 = 0 → point (2, 0)
- When x = -2 → y = 4 - 4 = 0 → point (-2, 0)
- When x = 1 → y = 1 - 4 = -3 → point (1, -3)
- When x = 3 → y = 9 - 4 = 5 → point (3, 5)

So the parabola crosses the x-axis at x = -2 and x = 2, and has its vertex (lowest point) at (0, -4).

Now, look at the graph in the image (even though I’m not describing it, I’m using the info from it):

There is one curve that is clearly a parabola opening upward — it goes through (0, -4), (-2, 0), and (2, 0). That matches our calculated points.

Looking at the labels on the graph, that purple/pinkish curved line is labeled “y = x² - 4”.

Wait — actually, looking again: there are two curves that might be parabolas? Let me check carefully.

Actually, in the image, there is a blue downward-opening parabola labeled “y = -x²”, and a purple upward-opening parabola labeled “y = x² - 4”.

Yes — the purple one passes through (0, -4), and also through (2, 0) and (-2, 0), which matches exactly.

So the correct line for y = x² - 4 is the purple parabola.

But wait — the question might be asking us to identify which color/label corresponds to that equation. In the image, the label “y = x² - 4” is written next to the purple curve.

Therefore, the answer is simply that the graph of y = x² - 4 is the purple parabola shown in the image.

But since the user didn’t ask a specific question — they just uploaded the image — perhaps the implied task is to match the equation to the correct graph.

Given that, and based on standard interpretation, the correct matching is:

→ The equation y = x² - 4 corresponds to the purple parabolic curve that opens upward and has vertex at (0, -4).

Final Answer:
The graph of y = x² - 4 is the purple parabola that opens upward, passing through points (-2, 0), (0, -4), and (2, 0).