I was just taught a formula to solve bijective functions, its shown below:

a[(x +b/2a)^{2 }- (b^{2 }- 4ac)/4a^{2}]

It was used to solve the following problem:

f(x) = 4x^{2 }- 2x + 3

write f(x) in the form f(x) = a(x-b)^{2}+ c, (where x > p if f is invertible)

I would like to know what the formula is and how it can prove the function is bijective.

I'm new so forgive me, if i break the rules. Thankyou.