If h>0 the graphs is horizontally translated h units to the right.
If h<0 the graphs is horizontally translated |h| units to the left.
We can now identify the value of the parameters by comparing our given function y=(x-3)^2 with the general form y = a(x-h)^2.
y= a(x- h)^2
y= (1)(x- 3)^2
For this case a=1 and h= 3. Therefore, the graph will be the same as the parent function f(x)=x^2, but translated 3 units to the right.
We can use a graphing calculator to verify our prediction.
As we can see in the graph above, the function y=(x-3)^2 is the same as that of f(x) =x^2 but shifted 3 units to the right, as predicted.
b We will proceed just as we did in Part A. First let's identify the parameters a and h for the given function y = (x+3)^2 by comparing it to the general form y = a(x-h)^2.
y= a(x- h)^2
y= (1)(x-( - 3))^2
Hence, for this case a=1 and h= - 3. Therefore, the graph will be just as that of the parent function f(x)=x^2 but translated 3 units to the left.
We can use a graphing calculator to verify our prediction.
As we can see in the graph above, the function y=(x+3)^2 is the same as that of f(x) =x^2 but shifted 3 units to the left, as predicted.
c We will proceed just as we did in previous in the parts. First let's identify the parameters a and h for the given function y = -(x-3)^2 by comparing it to the general form y = a(x-h)^2.
y= a(x- h)^2
y= (- 1)(x- 3)^2
Then, for this case a=- 1 and h= 3. Therefore, the graph will be similar to that of the parent function f(x)=x^2 but translated 3 units to the right, and reflected in the x-axis.
We can use a graphing calculator to verify our prediction.
As we can see in the graph above, the function y=-(x-3)^2 is the same as that of f(x) =x^2, but shifted 3 units to the right and reflected in the x-axis. This confirms our prediction.
