Quadratic Equation: Analyzing Graph of y=(5-2x)^2+1

[TyErd]

The graph of y=(5-2x)^2+1. What are the transformations that have occurred from y=x^2.

Im really confused with the transformations here.

 

[TyErd]

mainly confused about the dilation factor.

 

[TidusBlade]

For $$y=f(x)+b$$, the effect of changes in b is to translate the graph of $$y=f(x)$$ vertically through b units, so now you know what the +1 at the end does.

For $$y=f(kx)$$, $$k>0$$, the effect of changes in k is to horizontally stretch or compress the graph of $$y=f(x)$$ by a factor of $$1/k$$ , so that takes care of the 2x.

As you can see, everything in your transformed graph, including the minus sign does one simple translation, and combined you get your graph.

They're nicely summarized here and here's a more comprehensive explanation ;)

The dilation is due to the 2x, since every y-value is now doubled, it rises faster and so appears to have shrunk.

 

[TyErd]

The answer to this question is: dilation factor of 4 parallel to the y axis, translation of 2.5 to the right and 1 unit upwards.
Okay so what I did was change it into this y=[-2(x-5/2)]^2+1, but that gives me a dilation factor of 2 parallel to the y axis. What am I doing wrong?

 

[Pinu7]

This is actually really simple:
1. expand the squared quantity
2. Try to rewrite this function in the form of $$y=af(bx+c)+d$$ with f(x)=x^2
3. Use your textbook to interpret this answer.

 

[TyErd]

thankyou thankyou ! would this method work with all these type of questions?