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)

Question

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)

anonymous · Answer

@andras

anonymous · Answer

@offnenstudieren

anonymous · Answer

@phi please help me

phi · Answer

The 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)

phi · Answer

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)

phi · Answer

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) ?