How do you sketch the graph of #y=(x-4)^2# and describe the transformation?

Question

Avery Alexander · Accepted Answer

see below

The graph of #y = (x-4)^2# is plot{(x-4)^2 [-7.58, 12.42, -2.96, 7.04]} The transformation from the parent graph #y = x^2# can be seen as a shift 4 units to the right.

Hazel Anglin · Answer

See explanation

The first step in any transformation problem is identify the parent function. We know the function is a parabola since the variable has a power of #2#

To begin graphing, we can start with graphing the parent function (that is #y=x^2#) first and work our way up from there:
graph{x^2 [-10, 10, -2, 5]}

If we recall our transformation rules, we would know that the graph #y=(x-4)^2# means that we shift the entire function #color(red) 4# units to the #color(red)("right")# So our final function looks like this: graph{(x-4)^2 [-10, 10, -2, 5]}

Here is a graph with the original function and the final function just so you can see that all we really did was shift the function #4# units to the right: graph{(y-x^2)(-y+x^2-8x+16)=0 [-8.764, 11.24, -0.88, 6.12]}

This table on transformation rules may be of good use:

Genesis Allen · Answer

undefined To sketch the graph of $ y = (x - 4)^2 $, you start with the parent function $ y = x^2 $ and apply a horizontal translation of 4 units to the right. This means every point on the graph of $ y = x^2 $ is shifted 4 units to the right to create the graph of $ y = (x - 4)^2 $. The shape of the parabola remains the same, but its vertex is now at the point (4, 0).