Rewriting f(x) as a Transformation of g(x)

[halvizo1031]

Homework Statement

Can someone assist me with number 3 please...

Homework Equations

The Attempt at a Solution

I went ahead and rewrote f(x) in vertex form in terms of a,b, and c but I'm having a hard time writing down how f can be thought of as a transformation of g.

 

[Mark44]

What did you get? You have f(x) = ax² + bx + c. Complete the square to get this into a form so that you can recognize the translations and other transformations relative to the graph of y = x².

 

[halvizo1031]

i got a[x+(b/2a)]^2 - [(b^2)/4a] + c where h=-(b/2a) and k=c-[(b^2)/4a]

 

[Mark44]

i got a[x+(b/2a)]^2 - [(b^2)/4a] + c where h=-(b/2a) and k=c-[(b^2)/4a]

Shouldn't h be + b/(2a)?
So f(x) = a(x + b/(2a))² + c - b²/(4a)

Or, f(x) = a(x + h)² + k, with h = b/(2a) and k = c - b²/(4a).

You know what the graph of y = g(x) = x² looks like, right? How would you need to transform the graph of g to get the graph of f?