Quadratic equations
Quadratic equations
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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:
- 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 \[(x-a)(x-b) = 0\] then \[x-a=0 \quad \mbox{or} \quad x-b=0\] giving \[x=a \quad \mbox{or} \quad x=b\]
- Quadratic formula.
To do
- Quadratic Equations worksheet (sigma Mathematics and Statistics Support Coventry University)