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Revision:Quadratic functions, completing the Square, the discriminant and their graphsTSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics Revision Notes > Quadratic functions, completing the Square, the discriminant and their graphs Quadratic functions are polynomials of the 2nd degree. Polynomials being the term to describe the sum of different powers and constants multiplied by a coefficient.
Quadratic FunctionsThe general equation for a quadratic is Quadratic equations have two solutions. To Solve quadratic equations you to first put it in the form There are three ways to solve quadratics you need to be familiar with.
FactorisingIn the form
To solve one of the brackets much each 0, meaning
Completing the SquareStart by putting the equation in the form Take the example We then divide the b (6) by two, then put it in brackets with x, then square it. We must also make the constant within the outer brackets equal to 0, giving:
We bring the constant (-9) over to the other side, then divide by the a term (2), giving:
To finish off, we leave x on its own, giving: Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
x=-3\pm\sqrt{\frac{9}{2} Quadratic FormulaThe quadratic formula is This formula can be used when the equation is equal to 0 and in the form
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![2[x^2+6x]+9=0](http://www.thestudentroom.co.uk/latexrender/pictures/ef/ef236727b9c8dec23fe720407fee595d.png "2[x^2+6x]+9=0")
![2[(x+3)^2-9]+9=0](http://www.thestudentroom.co.uk/latexrender/pictures/4b/4b1e4f8342ef0c315033076c7b5335dd.png "2[(x+3)^2-9]+9=0")
