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

Find \(a+b+c\).

The Vertex of the parabola is \(P(x=-3,\ y=1)\)

\(\begin{array}{|rcll|} \hline \mathbf{ay^2 + by + c} &=& \mathbf{x} \quad | \quad x=-3,\ y=1 \\\\ a*(1)^2 + b*(1) + c &=& -3 \\ \mathbf{a + b + c} &=& \mathbf{-3} \\ \hline \end{array}\)

Start with the vertex form     x = a(y-k)^2 + h

where h, k is the vertex

x = a (y-1)^2 -3    Substitute a value from the graph to find a     use  -2, 2

-2 = a(2-1)^2 -3

a = 1

so your equation for the parabola is   x = (y-1)^2 -3    now expand the right side

x = y^2 - 2y+1   -3

x = y^2 - 2y -2      a =1   b = -2   c = -2      sum = -3