What effect will replacing x with (x−4)have on the graph of the equation y=(x−3)^2?

The graph is shifted four units to the right.

--------------------------

This question is solved using the shifting concept.

--------------------------

In this question:

The original function is:

Replacing x by x - 4 is equivalent to finding f(x - 4), and so:

Plotting functions f(x) and f(x-4), as in the end of this answer, it can be seen that the blue graph of f(x-4) is shifted four units to the right of the red graph of f(x).

A similar question is given here link

Step-by-step explanation:

Our equation is: y=(x-3)²

x should be replaced by x-4

The graph is still a parabola but with a different vertex

The vertex here is :

y'= 2x-14

solve y'=0

2x-14=0

2x=14

x=7

You can easily find it without derivating by dividing -14 by -2

since: x²-14x-49

a=1 b= -14  c=-49

-b/2a = 14/2 = 7

the image of 7 is:

y=(7-7)² = 0

so the coordinates of the new vertex are (7,0) and it's a maximum

since y">0

y'= 2x-14

y"= 2 wich is positive