Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.$f(x)=-\frac{1}{2} x^2+4 x-2$

Solution

Verified
Step 1
1 of 6

Remember that the graph of $f(x)=a(x-h)^2+k$ is a transformation of the graph of $f(x)=x^2$.

where

1. $|a|$ is the dilation of $f(x)$ If $a \gt 1$, the graph moves away from the $x$-axis. If $0 \lt a \lt 1$, the graph moves toward the $x$-axis.
2. $h$ is a horizontal translation of $f(x)$ in $|h|\mathrm{~units}$ If $h \gt 0$, the graph shifts to the right. If $h \lt 0$, the graph shifts to the left.
3. $k$ is a vertical translation of $f(x)$ in $|k|\mathrm{~units}$ If $k \gt 0$, the graph shifts upward. If $k \lt 0$, the graph shifts downward.

## Recommended textbook solutions #### Precalculus

2nd EditionISBN: 9780076602186Carter, Cuevas, Day, Malloy
8,886 solutions #### Advanced Mathematics: A Precalculus Approach

1st EditionISBN: 9780137157808Marvin E. Doubet, Merilyn Ryan, Mona Fabricant, Theron D. Rockhill
8,008 solutions #### Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,142 solutions #### Precalculus: Mathematics for Calculus

7th EditionISBN: 9781305071759 (2 more)Lothar Redlin, Stewart, Watson
9,608 solutions