How do you sketch the graph of $y=1/2x^2$ and describe the transformation?

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Answer 1 · 2018-07-25T19:26:07

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Please read the explanation.

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We have the quadratic equation: $color(red)(y=f(x)=(1/2)*x^2$

Consider the Parent Function: $color(blue)(y=f(x)=x^2$

The General Form of a quadratic equation is:

$color(green)(y=f(x)=a*(x-h)^2+k$ , where $color(red)((h,k)$ is the Vertex

The graph of $color(blue)(y=f(x)=x^2$

pass through the origin $color(blue)((0,0)$

and the graphs uses both Quadrant-I and Quadrant-II.

Let us now look at the transformation of the graph.

Consider the format : $color(blue)(y=f(x)=a*x^2$

$color(red)([0 < | a | < 1]$ results in a compression.

Since, in the problem,

$color(red)(y=f(x)=(1/2)*x^2$ ,

$color(green)(a=(1/2)$ ,

there will be a vertical compression toward the x-axis.

The graph is below:

Note that the graphs of

$y=f(x)=x^2$ and

$y=f(x)=(1/2)*x^2$

are available together to examine the transformation.

enter image source here

How do you sketch the graph of y=1/2x^2y=1/2x^2 and describe the transformation?