Write $x^2 + 6x - 7$ in the form $(x + a)^2 + b$ where $a$ and $b$ are integers. - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 3

To write the quadratic expression in the form $(x + a)^2 + b$, we start by isolating the quadratic and linear terms:

$x^2 + 6x - 7$

Next, we complete the square for the expression $x^2 + 6x$. We take half of the coefficient of $x$ (which is 6), square it, and add and subtract it within the expression:

$x^2 + 6x = (x^2 + 6x + 9) - 9 = (x + 3)^2 - 9$

Now, substituting back into the original expression:

$(x + 3)^2 - 9 - 7 = (x + 3)^2 - 16$

Thus, we have $a = 3$ and $b = -16$. Therefore, the final transformed expression is:

$(x + 3)^2 - 16$