### Transformation of Graphs - translation

- f(x) → f(x + a) - a translation in the negative x-axis by a
- f(x) → f(x - a) - a translation in the positive x-axis by a
- f(x) → f(x) + a - a translation in the positive y-axis by a
- f(x) → f(x) - a - a translation in the negative y-axis by a

E.g.1

Sketch y = x

^{2}+ 2x - 3 and find the following:- The line of symmetry
- The solutions when y = 0
- The coordinates of the minimum point
- The y-intercept

y = x^{2} + 2x - 3

By completing the square, y = (x + 1)^{2} - 4

1) Line of symmetry, x = -1

2) (x + 1)^{2} - 4 = 0 → x = -3 or x = 1

3) Turning point ~ (-1,-4)

4) y-intercept ~ (0,-3)

E.g.2

Sketch y = x

^{2}-4x + 3 and find the following:- The line of symmetry
- The solutions when y = 0
- The coordinates of the minimum point
- The y-intercept

y = x^{2} -4x + 3

By completing the square, y = (x - 2)^{2} - 1

1) Line of symmetry, x = 1

2) (x - 2)^{2} - 1 = 0 → x = 3 or x = 1

3) Turning point ~ (2,-1)

4) y-intercept ~ (0,3)

You can practise translation interactively with the following applet:

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