Are all quadratics of the form y = ax^2+bx +c and y = -ax^2+bx +c functions? Explain your answer.

Answer 1

No, all quadratics in x and y are of the form

ax^2 + bxy + cy^2 + dx + ey + f = 0

Now, if you want quadratics where y is expressed as a function of x, then all are of the form

y = ax^2 + bx + c

where a,b,c can be positive or negative. There's no need for -ax^2 + bx + c.