There are several functions that will give us the answer above. A linear function that fits this specification is f(x) = x + 6 and a quadratic function that fits this specification would be f(x) = x^2 + 12x + 36.
To find the linear function, start with a basic slope (m) of 1 (you could use any slope to find this, but 1 will be the easiest) and your ordered pair. Next you can solve for the equation.
y = mx + b
0 = (1)(-6) + b
0 = -6 + b
6 = b
Then you can write the equation using your slope and intercept.
f(x) = x + 6
To find a quadratic with just one x intercept, we know that we must have a double root. All quadratics have 2 roots, so to have only one intercept means we must have a double at that point. This point would be the one above. To solve, we would need to use the term (x + 6) and square it. We pick this term because it satisfies the point above.
f(x) = (x + 6)(x + 6)
f(x) = x^2 + 6x + 6x + 36
f(x) = x^2 + 12x + 36
There are many others, but this is 2 of them.
