AS/A2 Pure 2 Pure 3

P1 Topic 2: Algebra
Solution of simultaneous equations
Solution of the simultaneous equations:
y = mx+c y = x2+ ax + b
depend on whether or not the graphs interect. Use the interactive display to choose values for m, c, a and b. Decide on the number of points of intersection.

Can you find values for which the line just touches the curve? m= c= a= b=

Summary A straight line and a quadratic curve can have two crossing points one crossing point - they touch no crossing points 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