THE DISCRIMINANT

The discriminant is part of the quadratic formula, the bit inside the square root symbol. Although it doesn’t give us exact details where the graph would be drawn, it tells us about the nature of the graph, whether it crosses the x axis, touches the x axis at a point or doesn’t touch the x axis at all.
The square root symbol is also sometimes called a radical.
There are 4 main cases worth looking at.
The first and second are the discriminant > 0 giving 2 solutions which are rational or 2 solutions which are irrational.
The third being discriminant = 0 giving one repeated root solution and the fourth where the discriminant < 0 giving no real solutions. (We don’t say it gives no solutions, but no real solutions because in YR13 you will learn they are complex solutions and you need complex number theory for that).
A rational solution is where the discriminant value is a square number like 1,4,9, etc. That means the quadratic equation would result in an x value or root with a whole number solution.

The square root symbol is also sometimes called a radical.

There are 4 main cases worth looking at.

The first and second are the discriminant > 0 giving 2 solutions which are rational or 2 solutions which are irrational.

The third being discriminant = 0 giving one repeated root solution and the fourth where the discriminant < 0 giving no real solutions. (We don’t say it gives no solutions, but no real solutions because in YR13 you will learn they are complex solutions and you need complex number theory for that).

A rational solution is where the discriminant value is a square number like 1,4,9, etc. That means the quadratic equation would result in an x value or root with a whole number solution.