Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-13x+27$.
y = x^2 -18x + 27 + c
We want to find the vertex of
x^2 -18x + 27
x coordinate of the vertex = -(-18) /(2 * 1) = 9
Put this back into the function to find the y coordinate ofthe vertex
9^2 - 18(9) + 27 = -54
So ....to find c
-54 + c = 1
c = 55
+721 
