## Related questions with answers

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

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 6Remember that the graph of $f(x)=a(x-h)^2+k$ is a **transformation** of the graph of $f(x)=x^2$.

where

- $|a|$ 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.
- $h$ 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.
- $k$ 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.

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