Answer
Consider the quadratic function $f\left( x \right)=a{{x}^{2}}+bx+c,a\ne 0$. If $a>0$ , then f has a minimum that occurs at $x=-\frac{b}{2a}$. This minimum value is $f\left( \frac{-b}{2a} \right)$. If $a<0$ , then f has a maximum that occurs at $x=-\frac{b}{2a}$. The maximum value is $f\left( \frac{-b}{2a} \right)$.
Work Step by Step
For the quadratic equation with $f\left( x \right)=a{{x}^{2}}+bx+c$.
If $a>0$ , then the parabola opens upward and the function f has a minimum value that occurs at $x=-\frac{b}{2a}$.
Point $x=-\frac{b}{2a}$ is the lowest point of the parabolic function after that function’s value increases -- that is, the graph of the parabola increases.
If $a<0$ , then the parabola opens downward and the function f has a maximum value that occurs at $x=-\frac{b}{2a}$.
Point $x=-\frac{b}{2a}$ is the highest point before that function’s value decreases -- that is, the graph of the parabola increases in the negative side of the graph.
