Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.
y = x^2 -8x + (8 + c)
This is aparabols that turns upward
The x coordinate of the vertex = 8 / (2*1) = 4
And we want the associated y coordinate of the vertex to = 1
So
1 = (4)^2 - 8(4) + (8 + c)
1 = -16 + 8 + c
9 = c
+452 
