SOLUTION: Write equations for the following word statements. Complete transformations in the order given. a) The graph of f(x) = x^2 is expanded horizontally by a factor of 4, reflected in

Algebra ->  Equations -> SOLUTION: Write equations for the following word statements. Complete transformations in the order given. a) The graph of f(x) = x^2 is expanded horizontally by a factor of 4, reflected in       Log On


   

Question 1000183: Write equations for the following word statements. Complete transformations in the order given.
a) The graph of f(x) = x^2 is expanded horizontally by a factor of 4, reflected in the y-axis, translated 3 units to the left and translated 5 units upwards. Determine the equation of the transformed function g(x).
I'm confused as to how it should look when transformed in the order given, and the correct steps to do so. i know i should "simplify" the expression after each change but i cant seem to figure out how to simplify.
my answer: g(x)=(-1/4x+3)^2 +5
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2 as the start.

Expanded vertically by factor 4 would be y=4x%5E2, but HORIZONTALLY should be 4y=x%5E2.

Reflect accross the y-axis would be no real change. y-axis is the axis of symmetry for this up to now.

Move 3 unit leftward: 4y=%28x-%28-3%29%29%5E2.

Move 5 unit upward: 4%28y-5%29=%28x-%28-3%29%29%5E2.

Simplify and you are probably wanting to finish in standard form, so these steps...
4%28y-5%29=%28x%2B3%29%5E2
y-5=%281%2F4%29%28x%2B3%29%5E2
highlight%28y=%281%2F4%29%28x%2B3%29%5E2%2B5%29



If you called your original function f(x), then you could call you changed function something else, like g(x).