Family of Parabolas y=(x-p)²

When there is an $a$ before the parentheses, it indicates the slope of the parabola.
The larger the $a$, the closer the parabola will be to its axis of symmetry. Steeper - with a smaller opening.
The smaller the $a$, the farther the parabola will be from its axis of symmetry. Less steep - with a larger opening.

Let's see an example that shows the balance between the change in slope and horizontal shift:
For example, in the function 

$Y=\frac{1}{2} (X-2)^2$

the changes will be:
Shift of $2$ steps to the right
and the change in slope, The parabola will be less steep and with a larger opening
Let's see it in an illustration:

Graphical and Algebraic Solution when $y=0$

Algebraic Solution

when $y=0$ the expression inside parentheses must be equal to $0$.
$X$ must be equal to $P$ for the equation to be correct.

The graphical solution is the vertex of the parabola.
In a quadratic function of this form 
$Y=(X-p)^2$
in which the coefficient of $X^2$  is $1$,
the vertex of the parabola is composed of$Y=0$  and by$P$ which indicates the $X$ vertex.
$(0,P)$
Note that, when in the equation there is a minus sign before the$P$
indeed, it is positive and, when there is a plus sign before the $P$ it is, in fact, negative.