1. We are given the quadratic function $F(x) = x^2 - 6x + 5$. 2. We want to express it in the form $F(x) = (x + a)^2 + b$ where $a$ and $b$ are constants. 3. Start by expanding the right side: $$(x + a)^2 + b = x^2 + 2ax + a^2 + b.$$ 4. Match the expanded form to the given quadratic: $x^2 - 6x + 5 = x^2 + 2ax + a^2 + b.$ 5. By comparing coefficients, we get two equations: - Coefficient of $x$: $-6 = 2a$ implies $a = \frac{-6}{2} = -3$. - Constant term: $5 = a^2 + b = (-3)^2 + b = 9 + b$ so $b = 5 - 9 = -4$. 6. Therefore, $a = -3$ and $b = -4$. 7. The final form is $$F(x) = (x - 3)^2 - 4.$$