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An architect is drawing a scale model of a bridge support and begins by graphing
f(x)=x^(2). Through a series of transformations, she finds that
g(x)=-2(x-4)^(2)+3 best models the bridge support. Which value results in a vertical stretch and reflection in the
x-axis of the graph of
f(x)=x^(2) to give the bridge the correct orientation and shape in the drawing?

An architect is drawing a scale model of a bridge support and begins by graphing $\newline$ $f(x)=x^{2}$ . Through a series of transformations, she finds that $\newline$ $g(x)=-2(x-4)^{2}+3$ best models the bridge support. Which value results in a vertical stretch and reflection in the $\newline$ x-axis of the graph of $\newline$ $f(x)=x^{2}$ to give the bridge the correct orientation and shape in the drawing?

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Reflections of functions

Full solution

Q. An architect is drawing a scale model of a bridge support and begins by graphing

\newline

f(x)=x^{2}

. Through a series of transformations, she finds that

\newline

g(x)=-2(x-4)^{2}+3

best models the bridge support. Which value results in a vertical stretch and reflection in the

\newline

x-axis of the graph of

\newline

f(x)=x^{2}

to give the bridge the correct orientation and shape in the drawing?

Identify Functions: Identify the original function and the transformed function. $\newline$ Original function: $f(x) = x^2$ $\newline$ Transformed function: $g(x) = -2(x-4)^2 + 3$
Compare Forms: Compare the forms of $f(x)$ and $g(x)$ to determine the transformations. $f(x) = x^2$ can be transformed to $g(x)$ by applying a vertical stretch, horizontal translation, and reflection across the $x$ -axis.
Determine Stretch Factor: Determine the vertical stretch factor. The coefficient of $x^2$ in $f(x)$ is $1$ . In $g(x)$ , the coefficient of $(x-4)^2$ is $-2$ . The negative sign indicates a reflection across the $x$ -axis, and the magnitude of $2$ indicates a vertical stretch by a factor of $2$ .
Confirm Reflection: Confirm the reflection across the $x$ -axis. $\newline$ The negative sign in front of the $2$ in $g(x)$ confirms the reflection across the $x$ -axis.

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