Home > CCA > Chapter 11 > Lesson 11.1.2 > Problem11-22

11-22.

Given the quadratic function $f(x)=(x−3)^2$, find the new expression for each part below and describe the transformation.

See problem 11-10 for additional help.

1.  $f(x)−1$

Substitute $(x−3)^2$ for $f(x)$.
$f(x)−1$
$(x−3)^2−1$

$(x−3)^2−1$ or $x^2−6x+8$
Shifted down $1$.

1.  $−1·f(x)$

See the help for part (a).

Reflected over $x$-axis.

1.  $f(x−1)$

$(x−4)^2$ or $x^2−8x+16$

1.  $f(−1x)$

Substitute $−1x$ for $x$ in the original function.