# Simultaneous Equations and Quadratic Inequalities

- Author:
- pirsquared

- Topic:
- Equations, 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 inequalit
that represent the required interval(s).__ies__

## 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