Question

Given the graph of y=x^2, what are the zeros of the function after the transformation down 4 units and left 3 units?

Answer 1

When we shift the function down 4 units, the equation becomes

$y=x^2-4$

Which means that the zeroes are

$x^2-4=0\iff x^2=4 \iff x=\pm 2$

When we shift the function 3 units left, the zeroes are shifted as well:

x=2 becomes x=2-3=-1

and

x=-2 becomes x=-2-3=-5