Transforming y = x²: Shifting 4 Right and 3 Up

To solve this problem, we will apply transformations to the function $y = x^2$.

Step 1: Horizontal Shift
When a function is moved 4 units to the right, the $x$ value inside the function is replaced with $x - 4$. So, the transformation of $y = x^2$ becomes $y = (x - 4)^2$.

Step 2: Vertical Shift
When a function is moved 3 units upwards, we add 3 to the whole function. Applying this to our function from Step 1 gives us $y = (x - 4)^2 + 3$.

Therefore, after the required transformations, the equation representing the function moved 4 units to the right and 3 units upwards is $y = (x - 4)^2 + 3$.

Checking the multiple-choice options, the correct choice is:

:

$y=(x-4)^2+3$