The turning point on a quadratic function

often with functions you may be required to find the maximum or minimum point in a curve. This can be especially present in a quadratic function. These are functions that have an x raised to the power of two. Help plot a graph if necessary. 

The way of thinking about a maximum of minimum turning point is that it must be going from a negative/positive gradient to a positive/negative gradient around a point. Therefore at this point the gradient must be zero. This is the point where a tangent will be horizontal as it just touches the graph. Explain an example of a function like this.