Question

write an equation that translates stretched vertically by a factor of 3 down 5 units for the following transformation to y=x^{2}

Answer 1

To translate the function \( y = x^2 \) so that it is stretched vertically by a factor of 3 and then shifted down 5 units, we follow these steps:

1. **Vertical Stretch**: To stretch the function vertically by a factor of 3, we multiply the entire function by 3. This gives us:
\[
y = 3x^2
\]

2. **Vertical Shift Down 5 Units**: To shift the function down 5 units, we subtract 5 from the entire function. This results in:
\[
y = 3x^2 - 5
\]

Thus, the final equation representing the transformation of \( y = x^2 \) that is stretched vertically by a factor of 3 and then shifted down 5 units is:
\[
y = 3x^2 - 5
\]