AS/A2 Pure 2 Pure 3

P1 Topic 2: Algebra
Minimums and maximums and completing the square
When the equation of a quadratic graph is given in the form y=a(x-b)2+c, it is said to be in completed square form. Investigate the effect of changing a, b or c. Make a=1, b=2, c=3. What are the coordinates of the minimum turning point? Change a. Does the minimum turning point change? Make a=-2, b=-1, c=2. What are the coordinates of the maximum turning point now? Does this maximum point move if you change a? What is the connection between the coordinates of the minimum or maximum point and the values of a, b and c?

Summary When the equation of a quadratic graph is given in the form y=a(x-b)2+c: the curve has a maximum turning point if a<0 and a minimum if a>0 the coordinates of the turning point (also called the vertex) will be at (b,c) the curve has an axis of symmetry at x=b Based on free Java applets from JavaMath