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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 28, 2020
 #1
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Starting with this form:  y - k  =  a(x - h)2   where (h, k) is the vertex.

--->     y - 4  =  a(x - 2)2

 

Now, the problem is to find the value of a.

Use the point (1, 1)     --->     1 - 4  =  a(1 - 2)2     --->     -3  =  a(-1)2     --->   -3  =  a

 

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

 

Multiply this out:  y - 4  =  -3(x2 - 4x + 4)

                            y - 4  =  -3x2 + 12x - 12

                                 y  =  -3x2 + 12x - 8

 Apr 28, 2020

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