# Graphing Quadratic Functions - Maxima and Minima

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How to graph quadratic functions (maxima and minima)?

Maxima and Minima Part 1
This lesson shows how to find local maxima or minima for a quadratic relation using the Completing the Square Method.
The process of completing the square involves changing the first two terms of a quadratic relation of the form y = ax2 + bc + c into a perfect square while maintaining an equivalent form of the original equation.
Example:
Expand y = (x - 3)2 + 1 into standard form.
How do you put y = x2 - 6x + 10 back into the form y = (x - 3)2 + 1?

Maxima and Minima Part 2
This lesson shows how to find local maxima or minima for a quadratic relation using the Completing the Square Method.
Example:
Convert y = 2x2 + 16x + 29 into y = a(x - h)2 + k form.
State the vertex, direction of opening and graph the parabola.

Maxima and Minima Part 3
This lesson shows how to find local maxima or minima for a quadratic relation using the Completing the Square Method.
Example:
Convert y = -x2 + 10x - 18 into y = a(x - h)2 + k form.
State the vertex, direction of opening and graph the parabola.

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