Question

The parabola
\[y=x^2\] is shifted to the right by
\[8\] units.
What is the equation of the new parabola?
\[y=\]

Answer 1

To shift the parabola given by \( y = x^2 \) to the right by \( 8 \) units, we replace \( x \) with \( x - 8 \) in the equation.

The transformation can be expressed mathematically as follows:

\[
y = (x - 8)^2
\]

Now, if we expand this equation, we get:

\[
y = (x - 8)(x - 8) = x^2 - 16x + 64
\]

However, the new equation that directly represents the parabola shifted to the right by 8 units is:

\[
y = (x - 8)^2
\]

Thus, the equation of the new parabola is:

\[
\boxed{(x - 8)^2}
\]