In these tutorials I show you how we can use completing the square to show prove that a quadratic expression is positive or negative for all real values and also in the sketching of quadratic graphs, enabling the location of maximum or minimum points and the equation of the line of symmetry.
Proof for Quadratic Expressions being >0 or <0
Part 1: (+ax2 types)
Part 2: (-ax2 types)
Experiment with the Graph
Move the sliders in the graph below
See how p stretches the graph. See what happens for positive and negative values.
See how q translates the graph parallel to the x-axis.
See how r translates the graph parallel to the y-axis.