Question

How can you tell if a graph has a negative or positive discriminant?

Answer 1

When a graph has 2 x-intercepts, it will have positive discriminant & when a graph has NO x-intercepts, it will have negative discriminant.

Explanation:

In a quadratic equation, the discriminant is the value of
`b^2-4ac`. This is "under the square root sign" when solving using quadratic formula.

Thus, there can be 3 possibilities:

1. Discriminant is 0 ( 2 equal real roots - meaning 1 touching point at the x-axis in the graph)

2. Discriminant can be positive ( 2 distinct real roots - meaning 2 cutting point in the x axis)

3. Discriminant can be negative ( 2 complex roots - meaning NO cutting point in x-axis)

Thus, when a graph has 2 x-intercepts, it will have positive discriminant & when a graph has NO x-intercepts, it will have negative discriminant.