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 "\(ax^2+bx+c\)".
+23253 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
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