The x - coordinate of a point where a graph crosses the x - axis is called the x - intercept of the graph.

The portion of the quadratic formula that is under the radical sign ( b² - 4ac ) is called the discriminant. The discriminant can be used to determine the number of real - number solutions of a quadratic equation. The relationship between the discriminant and the number of real nuumber solutions is shown below:
If b² - 4ac > 0 : there are two solutions. They are
If b² - 4ac = 0 : there is one solution which is -b / 2a
If b² - 4ac < 0 : there are no real number solutions.

Examples:
a.) Find the x - intercept of the graph of y = 2x² - 3x - 5. Try factoring first.
2x² - 3x - 5 = 0
( 2x - 5 )( x + 1 ) = 0
x = 5 / 2 or x = -1
answer: the x - intercepts are (5 / 2) and -1

b.)Use the discriminant to determine the number of real number solutions.
-x² + 10x - 25 = 0
b² - 4ac = 10²- 4( -1 )( -25 )
= 100 - 100
= 0 (the discriminant is equal to zero)
answer: One solution