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• A quadratic equation is an equation which contains only one variable but that variable must only be raised to powers that are positive whole numbers with a maximum value of $$2$$, that is, of the form:
$y=ax^2+bx+c$
• Quadratic functions can be represented graphically by a curve called a parabola. • The parabola can take two forms:

1. a minimum turning point when ($$a>0$$)

2. a maximum turning point when ($$a<0$$)

• In order to sketch a parabola you need to know:

1. where it cuts the $$y$$-axis ($$y$$- intercept, i.e. $$x=0$$)

2. where it cuts the $$x$$-axis (if at all, i.e. $$y=0$$)

3. the coordinates of the turning point (axis of symmetry can be found $$x=-\frac{b}{2a}$$).

• There are two techniques available to solve quadratic equations:

1. Factorisation works on the principle that if the product of two expressions is zero then one or both of those expressions must be zero.
2. If $(x-a)(x-b) = 0$ then $x-a=0 \quad \mbox{or} \quad x-b=0$ giving $x=a \quad \mbox{or} \quad x=b$