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Let \(f(x)=\frac{(x-2)^2-9}{3}\). The equation y=f(x) is graphed, and the x and y-intercepts of the graph are connected to form a polygon. What is the area of that polygon?

 May 27, 2020
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The x-intercepts occur at  (-1,0)  and  (5,0).

The y-intercept occurs at (0,-5/3).

 

The figure is a triangle with base from  (-1,0)  to  (5,0)  --  a base length of  6.

The height is from  (0,0)  to  (0,-5/3)  -  a height of  5/3

 

Use the area formula for a triangle:  A  =  ½·base·height  to find the area

 May 27, 2020

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