Consider a quadratic function y = f (x) = ax^{2} + bx + c. Let's determine the values of x for which y is negative and the values of x for which y is positive.
According to the sign of the discriminant = b^{2} - 4ac, we can occur the following cases:
1º - > 0
In this case the quadratic function admits two distinct real zeros (x1 x2). The parable intersects the Ox axis at two points and the sign of the function is as shown in the graphs below:
when a> 0 |
y> 0 (x <x_{1} or x> x_{2})
y <0 x_{1} <x <x_{2}
when a <0 |
y> 0 x_{1} <x <x_{2}
y <0 (x <x_{1} or x> x_{2})
when a> 0 |
when a <0 |
3º - < 0
when a> 0 |
when a <0 |