AS/A2 Pure 2 Pure 3

P1 Topic 2: Algebra
y=c(x-a)(x-b)
Investigate the effect of changing a, b or c. Graphs like these are called quadratic graphs. Make sure that you are clear about these aspects of a quadratic graph: its basic shape its symmetry the number of places where the curve crosses the x-axis how the values of a, b and c affect the shape and position of the curve

Summary The curve is U-shaped The curve is symmetric about a vertical axis The values of a and b determine where the curve crosses the x-axis If the values of a and b are the same, then the curve touches the x-axis at this point. When c=0 the curve is linear When c>0 the curve is U-shaped When c<0 the curve is Ç-shaped Changing the value of c stretches the curve vertically Based on free Java applets from JavaMath