GeoGebra Classroom

# 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).

## 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: