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Determine the x-and y-intercepts, the symmetry andthe vertex, and then draw the graph....

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zuly12 | eNoter

Posted July 21, 2013 at 4:18 AM via web

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Determine the x-and y-intercepts, the symmetry and
the vertex, and then draw the graph. of  4(x-2)^2

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 21, 2013 at 4:43 AM (Answer #1)

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`y = 4(x-2)^2`

When y = 0 then we get the y intercept.

`0 = 4(x-2)^2`

`0 = (x-2)^2`

`0 = (x-2)`

`x = 2`

So x intercept is 2.

 

When x = 0 then we get the y intercept.

`y = 4(x-2)^2`

`y = 4(0-2)^2`

`y = 16`

So y intercept is y = 16.

 

For every value of x the value of `(x-2)^2>=0` . So the minimum of `(x-2)^2 = 0` and it comes when x = 2.

`y = 4(x-2)^2`

When x = 2 then y = 0. So minimum of y is 0 at x = 2. This is the vertex.

This is a quadratic function. Quadratic functions are symmetrical along its vertex. So ` y = 4(x-2)^2` is symmetrical along x = 2.

 

The graph of the function is as follows.

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