Given the function f (x) = 4 (x + 1) ^2 - 3, indicate the shifts that will affect the location of the vertex, and explain what effect they will have. Use complete sentences.

-f (x-2)

-f (x) - 2

-f (2x)

-2⋅f (x)

He first two are relatively easy. f (x-2) shifts it sideways (2 to the right in this case) f (x) - 2 shifts it straight down (by 2)

f (2x) means replace x with 2x in the original 4 (2x + 1) ^2 - 3 if you factor out the 2 from the square root you get 4*sqr (2) (x + ½) ^2 - 3 which is now in the form a (x - h) ^2 + k the vertex is now at (-½, - 3) (it used to be at (-1,-3) the "a" has gotten bigger, which makes the parabola "skinnier" (it goes up faster)

2•f (x) becomes 2 * (4 (x + 1) 2 - 3) = 8 (x+1) ^2 - 6 where is the vertex now? is this parabola fatter or skinnier than the original f (x) ?