Question

Assuming we have an upward-facing parabola describe the location of the vertex in relation to the x-axis (above, below, or on the x-axis) when your discriminant is negative, positive and zero.

a. Negative discriminant:

b. Positive discriminant:

c. Discriminant is zero:

Answer 1

a. Negative discriminant: above

b. Positive discriminant: below

c. Discriminant is zero: on

Explanation:

If the discriminant is negative, then there are no real zeros. We have an upward-facing parabola, then the vertex is located above the x-axis

If the discriminant is positive, then there are two different real zeros. We have an upward-facing parabola, then the vertex is located below the x-axis

If the discriminant is zero, then there is one zero. We have an upward-facing parabola, then the vertex is located on the x-axis