Simultaneous Equations and Quadratic Inequalities
Quadratic Inequalities - Key Facts
- Solve a quadratic inequality by first making a quadratic equation to find the critical values - 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 inequalities that represent the required interval(s).
Quadratic Inequalities - Test Yourself
Simultaneous Equations - Key Facts
- Simultaneous equations can always be solved by substitution - rearrange the 'easier' equation to make it or , 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, - will identify how many points of intersection there are:
- there are TWO points of intersection
- there is ONE point of intersection (the line is a tangent)
- there are NO points of intersection
Drag the red line below to see the changes to the discriminant when the two equations are solved simultaneously: