Summary on Applications of Relations and Functions
- The quadratic function of the form f(x) = ax2 + bx + c, if a > 0 the graph opens upward, then the function has a minimum value, where as if a < 0, the graph opens downward, then it has a maximum value.
- The minimum or the maximum value of a quadratic function is obtained at the vertex of its graph.
- If the quadratic equation ax2 +bx +c = 0, a ≠ 0 has discriminant b2 – 4ac < 0, then the equation has no real roots. Moreover,
- The solution set of ax2 + bx + c ³ 0 is the set of all real numbers if a > 0 and is empty set if a < 0.
- The solution set of ax2 + bx + c £ 0 is the set of all real numbers if a < 0 and is empty set if a > 0.