Question

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

the x+1 makes it go 1 to the left and
the -3 makes it go down 3

Answer 2

for f(x-2) it will shift your function 2 to the right
f(X)-2 all of the function is shifted down by 2
f(2x) makes it happen twice as fast so its compressed horizontally by 2
2(f(x)) makes all your y calues 2 times bigger so its stretched vertically by 2

Answer 3

for example

Answer 4

here is a way to picture it

Answer 5

suppose f(x)=x^2 okay
now f(x-2)=(x-2)^2
we know x^2 is a parabola and -2 will maek the parabola shift to the right by 2
but another way to see why it does shift by 2
lets change our axis
f(x-2)=f(a)=a^2
if a=x-2
then a+2=x
if u graph a,f(a) its just a parabola originating from (0,0)as its
f(a)=a^2
but we know this means in terms of x
its a+2 so the x version is shifted 2 to the right