AFOQT Practice Test

What does the discriminant of a quadratic equation indicate?

1. It determines the shape of the parabola

2. It tells how many real roots exist

3. It shows the direction the parabola opens

4. It provides the value of c

The correct answer is: It tells how many real roots exist

The discriminant of a quadratic equation, which is found in the quadratic formula \( ax^2 + bx + c = 0 \), is given by the expression \( b^2 - 4ac \). This value is crucial because it indicates how many real roots the quadratic equation has. When the discriminant is positive, there are two distinct real roots, meaning the parabola intersects the x-axis at two points. If the discriminant is zero, there is exactly one real root, which corresponds to a situation where the parabola touches the x-axis at a single point (also known as a double root). When the discriminant is negative, there are no real roots; instead, the solutions are complex, indicating that the parabola does not intersect the x-axis at all. Understanding the discriminant's role helps in graphing the quadratic and anticipating the behavior of the function regarding its roots, which is fundamental in algebra and calculus.