Math Snap

STEP 1

1. The quadratic equation has the form $ax^2 + bx + c = 0$.
2. The $x$-intercept occurs where the quadratic equation equals zero.
3. The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$.
4. The nature of the roots of the quadratic equation is determined by the discriminant:
- If the discriminant is positive, there are two distinct real roots.
- If the discriminant is zero, there is exactly one real root (a repeated root).
- If the discriminant is negative, there are no real roots (complex roots).

STEP 2

1. Analyze the given information about the $x$-intercept.
2. Determine the implications for the discriminant.
3. Select the correct statement about the discriminant.

STEP 3

Analyze the given information. Since $x = -3$ is the only $x$-intercept, the quadratic equation has exactly one real root at $x = -3$.

STEP 4

Determine the implications for the discriminant. If there is exactly one real root, the discriminant must be zero because a zero discriminant indicates a repeated root.

Select the correct statement about the discriminant. Based on the analysis, the discriminant is $0$.
The statement that best describes the discriminant of the equation is:
The discriminant is 0.