Linear Transformations Quadratic Functions

Is the pictured graph growth, decay, or linear or quadratic?  

What type of function is shown?

Is this function linear or non linear?

Which parent function matches the graph?

"b" causes the parabola to horizontally ​ (a)   when $$b>1$$ .

"b" causes the parabola to horizontally*​ (a)   when $$b<1$$ .

*TYPO ON PACKET

$$The\ parent\ function\ f\left(x\right)\ =\ x^2$$ has translated by reflecting (a)   ​ and moving (b)   and to the ​ (c)  

the final equation would look like ​ (d)  

If the blue graph is
f(x) = x² 
then the red must be...

The parent function, f(x), is transformed so that it maps into g(x). Which equation would correctly represent g(x)?