Asked by Ian
Use Desmos to match each quadratic equation to the description of how its graph interacts with the x-axis. The quadratic equations are x^2+x+5=0, x^2-6x+9=0, and x^2-4=0 and the x-axis are the graph touches the x-axis at a single point, The graph does not cross or touch the x-axis, and the graph intersects the x-axis at two different points.
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Answered by
GPT-5 mini
AI
Matches (with brief reason):
- x^2 + x + 5 = 0 → The graph does not cross or touch the x-axis.
- Discriminant = 1 − 20 = −19 < 0 so no real roots.
- x^2 − 6x + 9 = 0 → The graph touches the x-axis at a single point.
- Discriminant = 36 − 36 = 0 so one repeated root (x = 3).
- x^2 − 4 = 0 → The graph intersects the x-axis at two different points.
- Factor: (x − 2)(x + 2) = 0 so roots x = −2 and x = 2.
- x^2 + x + 5 = 0 → The graph does not cross or touch the x-axis.
- Discriminant = 1 − 20 = −19 < 0 so no real roots.
- x^2 − 6x + 9 = 0 → The graph touches the x-axis at a single point.
- Discriminant = 36 − 36 = 0 so one repeated root (x = 3).
- x^2 − 4 = 0 → The graph intersects the x-axis at two different points.
- Factor: (x − 2)(x + 2) = 0 so roots x = −2 and x = 2.
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