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Find the equation whose graph is a parabola with vertex (2,4), vertical axis of symmetry, and contains the point (1,1). Express your answer in the form "\(ax^2+bx+c\)".

 Apr 17, 2020
 #1
avatar+20812 
+1

The graphing form is:   y - k  =  a(x - h)2   where the vertex is (h, k)  =  (2, 4).

--->   y - 4  =  a(x - 2)2  

 

To find a, substitute the values of (1, 1) into the above form:

--->   y - 4  =  a(x - 2)2   --->    1 - 4  =  a(1 - 2)2   --->   -3  =  a(-1)2   --->   -3  =  a

 

So, the equation is:  y - 4  =  -3(x - 2)2 

 

To get this into the desired form:  y - 4  =  -3(x2 - 4x + 4)   --->   y - 4  =  -3x2 + 12x - 12

--->   y2  =  -3x2 + 12x - 8

 Apr 17, 2020
 #2
avatar+12182 
+1

Find the equation whose graph is a parabola with vertex (2,4), vertical axis of symmetry, and contains the point (1,1).

laugh.

 Apr 17, 2020

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