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The red parabola shown is the graph of the equation \(x = ay^2 + by + c\). Find c.

 

 Apr 16, 2020
edited by Guest  Apr 16, 2020
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The graphing form of the equation is:  x - h  =  a(y - k)2

where  (h, k)  =  (-4, 2)  is the vertex:  x - -4  =  a(y - 2)2   --->   x + 4  =  a(y - 2)2​  

 

To find the value of a, put in the coordinates of a point on the parabola -- I'm going to choose the point (-2, 0):

--->    x + 4  =  a(y - 2)2​    --->   -2 + 4  =  a(0 - 2)2​   --->   2  =  a(4)   --->   a  =  ½

 

The final equation is:   x + 4  =  ½·(y - 2)2​  

 

Multiplying this out:     x + 4  =  ½·(y2 - 4y + 4)

                                    x + 4  =  ½·y2 - 2y + 2

                                          x  =  ½·y2 - 2y - 2

 Apr 17, 2020

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