Question

F(x)=x^2+6x+8 (i) complete the square to rearrange f(x) in the form f(x)=(x+a)^2-b where a and b are positive integers? (ii) hence explain how the graph o f can be obtained from the graph of y=x^2 by using appropriate translations?

Answer 1

see below graph{x^2+6x+8 [-10, 10, -5, 5]}

Explanation:

`F(x)=x^2+6x+8`

(i) Completing the square; half the coefficient of `x` add and subtract as follows:

`F(x)=(x^2+6x+color(red)(3^2))+8color(red)(-3^2)`

`F(x)=(x+3)^2-1`

(ii) In general

`F(x+a)+b" "`is a translation by the vector `((-a),(b))`

of the function `F(x)`

`:.F(x)=(x+3)^2-1" is obtained by the translation vector"`

`((-3),(-1))`from the graph `y=x^2`