Quadratic equations
Quadratic equations

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:
 a minimum turning point when (\(a>0\))
 a maximum turning point when (\(a<0\))
 a minimum turning point when (\(a>0\))
 In order to sketch a parabola you need to know:
 where it cuts the \(y\)axis (\(y\) intercept, i.e. \(x=0\))
 where it cuts the \(x\)axis (if at all, i.e. \(y=0\))
 the coordinates of the turning point (axis of symmetry can be found \(x=\frac{b}{2a}\)).
 where it cuts the \(y\)axis (\(y\) intercept, i.e. \(x=0\))
 There are two techniques available to solve quadratic equations:
 Factorisation works on the principle that if the product of two expressions is zero then one or both of those expressions must be zero. If \[(xa)(xb) = 0\] then \[xa=0 \quad \mbox{or} \quad xb=0\] giving \[x=a \quad \mbox{or} \quad x=b\]
 Quadratic formula.