Translating graphs
The translation of graphs is explored
Translations parallel to the y-axis
A translation is a shift of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis.
If \(f(x) = x^2\), then \(f(x) + a = x^2 + a\).
The value of \(a\) represents a vertical shift in the graph. As \(a\) increases, the graph shifts upwards. As \(a\) decreases, the graph shifts downwards.
Example one
\(f(x) = x^2\)
\(f(x) + 3 = x^2 + 3\)
Example two
\(f(x) = x^2\)
\(f(x) - 2 = x^2 - 2\)
\(f(x) + a\) represents a translation through the vector \(\begin{pmatrix} 0 \\ a \end{pmatrix}\).
Translations parallel to the x-axis
If \(f(x) = x^2\) then \(f(x + a) = (x + a)^2\).
The value of \(a\) represents a negative horizontal translation in the graph. If \(a\) is positive, then the graph will translate to the left. If \(a\) is negative, then the graph will translate to the right.
Example one
\(f(x) = x^2\)
\(f(x + 3) = (x + 3)^2\)
Example two
\(f(x) = x^2\)
\(f(x - 2) = (x - 2)^2\)
\(f(x + a)\) represents a translation through the vector \(\begin{pmatrix} -a \\ 0 \end{pmatrix}\)
More guides on this topic
- Equations of lines – WJEC
- Equations of curves - Intermediate & Higher tier – WJEC
- Basic algebra – WJEC
- Equations and formulae – WJEC
- Factorising - Intermediate & Higher tier – WJEC
- Quadratic expressions - Intermediate & Higher tier – WJEC
- Sequences – WJEC
- Inequalities - Intermediate & Higher tier – WJEC
- Simultaneous equations - Intermediate & Higher tier – WJEC