# How do you determine whether there are two, one or no real solutions given the graph of a quadratics function intersects the x axis twice?

##### 1 Answer

Please see below.

#### Explanation:

Assume the quadratic function to be

**Two real solutions**

If it cuts

As

=

= **................(A)**

there could be two values of

Example: Shows two graphs each for different parameters. While one opens upwards other opens downward.

graph{(y-3x^2+7x-3)(y+x^2+2x-1)=0 [-3.854, 6.146, -2.66, 2.34]}

**One real solution**

In such a case the quadratic function touches **(A)**, if it is so, we get

Examples: graph{(y-x^2+2x-1)(y+x^2+4x+4)=0 [-3.854, 6.146, -2.66, 2.34]}

**No real solution**

In such a case the quadratic function does not touch / cut **(A)**, as

Examples: graph{(y-x^2-3x-3)(y+x^2-3x+3)=0 [-3.854, 6.146, -2.66, 2.34]}