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