[list][*]Solve a quadratic inequality by first making a quadratic equation to find the [b]critical values[/b] - the points at which the graph changes from positive to negative, and vice versa.[/*][*]Draw a sign diagram to represent three intervals, and determine for each interval if the graph is positive or negative.[/*][*]State the inequality OR inequalit[b][u]ies[/u][/b] that represent the required interval(s).[/*][/list]

[list][*]Simultaneous equations can always be solved by substitution - rearrange the 'easier' equation to make it [math]y=\ldots[/math] or [math]x=\ldots[/math], then substitute it into the 'harder' equation.[/*][*]Use these to find the points of intersection between a line and a curve or a circle and a curve.[/*][*]The discriminant - remember, [math]b^2-4ac[/math] - will identify how many points of intersection there are:[br] [math]b^2-4ac>0[/math] - there are TWO points of intersection[br] [math]b^2-4ac=0[/math] - there is ONE point of intersection (the line is a [b]tangent[/b])[br] [math]b^2-4ac<0[/math] - there are NO points of intersection[br][/*][/list][br]Drag the red line below to see the changes to the discriminant when the two equations are solved simultaneously: