AFOQT Practice Test

When is the vertex of a parabola located on the x-axis?

1. When the discriminant is positive

2. When the discriminant is negative

3. When the discriminant is zero

4. When a is less than 0

The correct answer is: When the discriminant is zero

The vertex of a parabola is located on the x-axis when its y-coordinate is zero, which occurs when the quadratic equation has a double root. This situation is indicated by the discriminant being zero. In the context of a quadratic equation in the form of \(ax^2 + bx + c = 0\), the discriminant is given by the expression \(b^2 - 4ac\). When the discriminant equals zero, it indicates that there is exactly one real root, meaning the parabola touches the x-axis at its vertex. This is a characteristic of a parabola that is tangent to the x-axis. The presence of a positive or negative discriminant indicates different behaviors of the roots; a positive discriminant indicates two distinct real roots, while a negative discriminant indicates no real roots. The condition regarding the coefficient 'a' being less than 0 speaks to the orientation of the parabola but does not determine whether the vertex is on the x-axis. Thus, the correct condition for the vertex to lie on the x-axis is indeed when the discriminant is zero.