**Discriminant.**The Quadratic Equation has a degree to the power 2 (when we say x squared). We say quadratics are polynomials of the degree 2, in the form of ax^2 + bx + c. Where a,b,c are constants, and a is not 0. The graph of a quadratic is a parabola, almost a U shape, like this :

The shape of a parabola |

When

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**a (coefficient of is***x*^{2})is positive, a U shaped parabola will be the graph**This is one of the transformation of functions, I will be showing you in a later post ( which results in a reflection in the x-axis)**

__When a is negative, it will be an upside down U.__^{}

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^{Where this curve, crosses the x-axis, are known as the roots. These roots are the "solutions" when we solve these functions as equations by equalling them to 0, and using one of the 3 methods.}

^{The Discriminant }

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^{The Discriminant, is an expression, which allows us to find out the nature of the roots of a quadratic equation. It is given by : }

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^{There are 3 possibilities of the discriminant :}

^{* Discriminant > 0 (This means the quadratic has two distinct real roots)}

^{*Discriminant < 0 (This means the quadratic has two distinct complex / no real roots)}

^{*Discriminant = 0 (This means the quadratic has 1 real root / repeared root)}

^{I shall provide all three posibilities with an example, an my image notes, along with some graphs.}

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