The standard form of a quadratic equation is ax2+bx+c where a, b, and c are constants. But a is not zero. For a=0 the
equation no longer remains a quadratic, instead it becomes a linear equation.
The graph of a quadratic function is called a parabola.
If a>0, the parabola opens upward. So, the graph has a minimum point.
If a<0, the parabola opens downward. So, the graph has a maximum point.
The maximum/minimum points are also known as stationary points or turning points.
How to Find the Range of a Quadratic Function
Identify the standard form of the given quadratic function if not given.
Find the y-coordinate of the minimum/maximum point.
If the vertex is minimum point then range, y≥y-coordinate value found in step-2.
If the vertex is maximum point then range, y≤y-coordinate value found in step-2.
Finding a suitable Domain for a Quadractic function in order that Inverse function exists
Find the x-coordinate of the vertex of the quadratic function.
Restrict the domain to ≥ the x-coordinate of the vertex or ≤ the x-coordinate of the vertex.