12 parabolas

Given that two of the parabolas have the equations \[y = x^2 - 12x + 27\] and \[y = -x^2 + 12x - 36,\] can you find the equations of the other parabolas?

Can you factorise these equations? What does this tell you about the graphs of these two functions?

What is the difference between the graphs of \(y=x^2+bx+c\) and y=\(-x^2-bx-c\)? Can you spot any graphs in the picture that might satisfy such a relation?

If you know that a graph has equation \(y=ax^2+bx+c\), what is the equation of its reflection in the \(y\)-axis?