When given a quadratic equation:
ax^2+bx+c=0, a\neq 0
The points where the graph intersects the x-axis are called roots or zeros or solutions, which can be easily found with this quadratic formula:
Usually the following is defined:
Then it’s easy to see from the formula that the equation has 2 roots when
That means the graph crosses the x-axis twice.
The equation has one root when
Which means the graph crosses the x-axis exactly once.
And it has no real roots when
And that means the graph doesn’t cross the x-axis at all.
In addition, the roots of the equation also follow these formulas:
Also, with the roots you can factor the quadratic equation as follows: