5. y = x^2 - 8x + 17

This is a quadratic equation. The graph is a parabola. The vertex can be found at x = -(-8)/(2*1) = 4. The y-coordinate of the vertex is 4^2 - 8*4 + 17 = 16 - 32 + 17 = 1. The vertex is at (4, 1).