Translation by x

[mikexz]

How do you graph a function which has x as a translation without using a table of values.

e.g. f(x)=x^2+x


thanks

 

[skeeter]

you need to get the quadratic in the form ...

y = (x - h)² + k

the vertex of the parabola y = x² will be translated to the position (h,k)

you complete the square to accomplish this ...

y = x² + x

y = [x² + x + (1/4)] - (1/4)

y = [x + (1/2)]² - (1/4)

the vertex of this parabola is at (-1/2, - 1/4) ... the parent graph of y = x² is shifted left 1/2 unit and down 1/4 unit.