The parabola

Question

\[y=x^2\] is scaled vertically by a factor of

\[\dfrac{2}3\].
What is the equation of the new parabola?
\[y=\]

Answer 1

To scale the parabola \( y = x^2 \) vertically by a factor of \( \frac{2}{3} \), we need to multiply the entire equation by this factor.

Starting with the original equation:

\[ y = x^2 \]

We multiply the right-hand side by \( \frac{2}{3} \):

\[ y = \frac{2}{3} x^2 \]

Thus, the equation of the new parabola is:

\[ y = \frac{2}{3} x^2 \]