+177 The red parabola shown is the graph of the equation \(x = ay^2 + by + c\). Find \(a + b + c\).
Each tick mark on the graph is one unit.
Start with the vertex 5,-4
vertex form x= a (y+4)^2 +5 use point (3,-2) to calc a = - 1/2
x = -1/2 (y+4)^2 + 5
+129852 We have the form
x = - a ( y - k)^2 + h
And the vertex = (5, -4) = (h, k)
x = -a ( y - - 4)^2 + 5
x = -a ( y + 4)^2 + 5
We know another point on the graph ( -3, 0)
So....we can solve for a
-3 = -a ( 0 + 4)^2 + 5
-3 - 5 = -a ( 16)
-8 = -a (16)
-8/-16 = a
1/2 = a
So we have
x = (-1/2) ( y + 4)^2 + 5 expand this
x= (-1/2) ( y^2 + 8y + 16) + 5
x = (-1/2)y^2 -4y -8 + 5
x = (-1/2)y^2 - 4y -3
a + b + c = (-1/2) - 4 - 3 = -7 1/2 = - 15/2
Here's a graph : https://www.desmos.com/calculator/fxczjujb5g
