Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)

For example, in the function:
$y=(x-4)^2+3$

The changes will be:
according to $P=4$ -The parabola will shift $4$ steps to the right.
According to $K=3$ -The parabola will shift $3$ steps upwards.

Let's see it in the illustration:

We can see that the vertex of the parabola is:
$(4,3)$

Zero Point or Root of the Function - Graphical and Algebraic Solution when $Y=0$

The zeros of a function are the intersections with the $X$ axis.

when $K$ positive - This equation has no solution except in the case where $K$ equals$0$ and also $P$ equals$X$.
when $K$ negative- Generally, this equation will have $2$ solutions.

The graphical solution are the points of intersection of the parabola with the $X$ axis
that is, the zeros of the function.