Zero (Quadratic Functions)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A zero of a quadratic function is a value of x that makes the quadratic equation equal to zero. In other words, it is a solution to the equation ax^2 + bx + c = 0.
The zeros of a quadratic function are the x-intercepts of the graph of the quadratic, meaning the points where the parabola crosses the x-axis. These points represent the values of x where the output of the quadratic function is zero.
Key points about zeros:
A quadratic function can have:
Two zeros: If the parabola crosses the x-axis at two points.
One zero: If the parabola touches the x-axis at exactly one point (the vertex).
No zeros: If the parabola does not cross the x-axis at all (the graph is either entirely above or below the x-axis).
2 | 1 | 0 |
|---|---|---|
 |  |  |
Example:
For the quadratic equation x^2 - 5x + 6 = 0, the zeros can be found by factoring:
(x - 2)(x - 3) = 0
So, the zeros are x = 2 and x = 3. These are the values of x where the quadratic equation equals zero, and they represent the points where the graph of the quadratic crosses the x-axis.
In summary, the zeros of a quadratic equation are the values of x that make the quadratic function equal to zero, and they correspond to the x-intercepts of the parabola.