Ok so you are correct that x is input and y is output the you could be talking about a function in general or a kind of function normally used called a one-to-one function which I will assume you are talikning about
one-to-one funciton has that for every input, there is only 1 output, ie, x never repeats with a diffent y example (1,2), (2,2) is a function since x didn't repeat (1,2), (1,3) is not since x repeats with a different y
points given are
(-5,1),(-3,-2), (3,0),(1,1),(2,0),(6,4)(8,-2),(8,7) we see that the points (8,-2) and (8,7) make it not a function since it is the same input (8) that gives 2 different outputs
When the leading coefficient is 1, If the constant ( c term) is a perfect square and the b term is 2* the square root of the c term. Ex. x*2 + 10x + 25 2*5 = 10 5*5=25 Ex. x^2 - 12x + 36 2 * -6 = -12 6*6=36