The graph of g is a vertical shrink by a factor of 13and a reflection in the y-axis, followed by a translation 3 units right of the graph of f(x)=x2. Write a rule for g. Then identify the vertex.

Answer 1

Monze,

We know f(x)=x². Starting there, a vertical compression by a factor of 13 is g(x)=(1/13)x². Flip it over the y axis by making x negative in the parentheses: g(x)=(1/13)(-x)². Finally, translate it right three by adding three to the negative x: g(x) = (1/13)(-x+3)².

You'll note that we're adding three to x here, instead of subtracting as we normally would to translate a graph to the right, and that's because of the reflection over the y axis.

Normally, the vertex of the parent function y=x² is at (0,0). Shrinking it did nothing to the vertex, and reflecting it over the y axis also doesn't change that point. Only translating the function right three changes the vertex, which is now at (3,0).

I hope this helps! Have fun mathing, and get in touch if you need anything else.

LizZ