+743 Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c+x^2-8x$.
+129895 Simplifying f(x) we have
2x^2 -13x + c
This will be a parabola that turns upward.....we can let the vertex lie on the line y =1
The x coordinate of the vertex is (13 / 4)
And we want the function to = 1 ......so......
2(13/4)^2 - 13(13/4) + c = 1
2(169) / 16 - 169 / 4 + c = 1
169 / 8 - 169/ 4 + c = 1
-169/ 8 + c = 1
c = 1 + 169/8
c = 8/8 + 169/8
c = 177 / 8 = 22.125
