AS/A2 Pure 2 Pure 3

P1 Topic 2: Algebra
y=ax2+bx+c
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

Summary Make sure you understand what quadratic curves can look like, so that you could easily sketch one if given its equation. Usually, in advanced level mathematics, we sketch graphs rather than plot them. This means that we draw - carefully - a diagram which shows the essential shape of the graph, including any obvious symmetries, and marking clearly where the graph crosses the axes. When a=0 the curve is linear When a>0 the curve is U-shaped When a<0 the curve is Ç-shaped The curve is always symmetric, with a line of symmetry going down through the middle The value of c determines the y-intercept When a is non-zero, the curve may cross the x-axis at 0,1 or 2 places Based on free Java applets from JavaMath