### Home > INT3 > Chapter 5 > Lesson 5.2.2 > Problem5-72

5-72.

Given $f(x)=-2(x-1)^2+3$, state the equation of the parent graph. Then describe how $f(x)$ is transformed from the parent graph.

Pay attention to the expression in the parentheses and also its exponent.

$y = x^2$

The graph of $y = f(x)$ is reflected over the $x$-axis to open downward, stretched vertically by a factor of $2$, and then translated $1$ unit right and $3$ units up to have a vertex at $(1, 3)$.