If the discriminant is greater than zero, how many x intercepts does the graph of the quadratic function have?

When analyzing the number of x-intercepts for a quadratic function based on its discriminant, it is important to understand the implications of the value of the discriminant in the quadratic formula. The discriminant is calculated as ( b^2 - 4ac ) from the general form of a quadratic equation ( ax^2 + bx + c = 0 ).

A discriminant greater than zero indicates that the quadratic equation has two distinct real solutions. This is because the positive value allows the square root in the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) to yield two different values for ( x ), corresponding to the two different x-intercepts on the graph of the function.

Consequently, when the discriminant is greater than zero, the graph of the quadratic function will intersect the x-axis at two points, confirming that it indeed has two x-intercepts. This characteristic is fundamental to understanding the behavior of quadratic functions and their graphs.