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

Jul 25, 2018

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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)

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

$y = f \left(x\right) = {x}^{2}$ and

$y = f \left(x\right) = \left(\frac{1}{2}\right) \cdot {x}^{2}$

are available together to examine the transformation.