Observe the nature of the roots and the discriminant. What relationship do you observe between the nature of the roots and how the curve intersects the x-axis?

Question

I don't know what to write for this question because I don't get what it means by how the curve intersects the x-axis.

Answer 1

The discriminant is b² - 4ac, which you find from the quadratic equation: y = ax² + bx + c.

If the discriminant > 0, there are two unequal, real roots. This means the parabola intersects the x-axis in two places.

If the discriminant = 0, there is one root of multiplicity 2. This means the parabola intersects the x-axis in one place.

If the discriminant < 0, there are no real roots. This means the parabola does not intersect the x-axis since there are two complex roots.