Showing transformations from y=x² to f(x)=-(3+x)²+1

[Faith S]

One of my homework questions said "Explain how to obtain f(x)=-(3+x)^2+1 from the graph of y=x^2."
I know somehow you need to move the graph right 3, reflect about the x-axis, and move up one, but I don't know how to factor and manipulate the equation to show this.

 

[jedishrfu]

Define an x' and a y' so that your equation looks like the y=x^2 format.

 

[Ray Vickson]

One of my homework questions said "Explain how to obtain f(x)=-(3+x)^2+1 from the graph of y=x^2."
I know somehow you need to move the graph right 3, reflect about the x-axis, and move up one, but I don't know how to factor and manipulate the equation to show this.

Your description is perfectly OK as is. However, be careful about moving the graph---right or left?