Answer
The function\[y=a{{x}^{2}}+bx+c\ \text{or}\ f(x)=a{{x}^{2}}+bx+c\],\[a\ne 0\] is called a\an quadratic function. The graph of this function is called a\an parabola. The vertex or turning point occurs where\[x=\frac{-b}{2a}\].
Work Step by Step
The provided function is \[y=a{{x}^{2}}+bx+c\ \text{or}\ f(x)=a{{x}^{2}}+bx+c\] and the degree of the provided function is 2, therefore, the provided function is quadratic.
The shape of the graph obtained with the functional value of the provided function corresponding to the values of \[x\] is of the parabola.
Therefore, the graph of the function is called parabola.
For the values of \[x\]on the left of the \[x=\frac{-b}{2a}\] graph of the function decreases and for the values of\[x\]on the right of \[x=\frac{-b}{2a}\] the graph of the function increases.
Therefore, the point \[x=\frac{-b}{2a}\] is the turning point or vertex of the graph of the provided function.
