Question 1125845
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<pre>
A parabola with the vertex (3,4) has the form


    y(x) = {{{a*(x-3)^2 + 4}}}.


The only unknown is the coefficient "a".


To find it, use the fact that the point (1,-8) lies on the graph.  It gives you an equation


    -8 = {{{a*(1-3)^2 + 4}}},   or

    -12 = 4a.


Hence,  a = {{{-12/4}}} = -3.


<U>Answer</U>.  The function is  y(x) = {{{(-3)*(x-3)^2+4}}}.
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Solved.