dilation question

[hardworker]

Can anyone explain why the dilation for this question is 12 and why it occurs in the x axis.

y=3(2x-3)^2-0.25 please could u also explain how the dialation would occur  in the y-axis for this question  and how a reflection can occur in the y axis too.  Because dilation and reflection really confuse the hell out of me. Thanks in advance.

[brightsky]

y=3(2x-3)^2 - 1/4 = 3[2(x-3/2)]^2 - 1/4 = 3*2^2*(x-3/2)^2 - 1/4 = 12*(x-3/2)^2 - 1/4
so dilation from x-axis by a factor of 12.

consider the general function y = f(x)
dilation from x-axis by a factor of k: y/k = f(x) or in other words y = k*f(x) --> notice that y becomes y/k
dilation from y-axis by a factor of k: y = f(x/k) --> notice that x becomes x/k

[hardworker]

Im just confused about the part where you squared the 2 so it became 4 and hence multiplied it by 3 to get 12 where did you get the other 2 from?

y=3(2x-3)^2 - 1/4 = 3[2(x-3/2)]^2 - 1/4 = 3*2^2*(x-3/2)^2 - 1/4 = 12*(x-3/2)^2 - 1/4
so dilation from x-axis by a factor of 12.

consider the general function y = f(x)
dilation from x-axis by a factor of k: y/k = f(x) or in other words y = k*f(x) --> notice that y becomes y/k
dilation from y-axis by a factor of k: y = f(x/k) --> notice that x becomes x/k

[brightsky]

a reminder that (a*b)^n = a^n*b^n

[Zealous]

Im just confused about the part where you squared the 2 so it became 4 and hence multiplied it by 3 to get 12 where did you get the other 2 from?

If you are still confused...
I'm just going to show you it without the -1/4, easier to type.



. Take out the 2, note it is still underneath the square.

Square the 2 to get 4 in order to take it out of the brackets.

Multiply out and wallah, that's what bright skywas implying by showing the rule.