Question 12 Rewrite x^2+8x-7 in the form (x-h)^2+k by completing the square. (x-4)^2+23 (x+4)^2+23 (x+4)^2-23 (x-4)^2-23

## Step 1: Group the $x$ terms<br />### Isolate the terms with $x$. $x^2 + 8x - 7 = (x^2 + 8x) - 7$<br /><br />## Step 2: Complete the square for the $x$ terms<br />### To complete the square for $x^2 + 8x$, take half of the coefficient of the $x$ term (which is 8), square it $(8/2)^2 = 4^2 = 16$, and add and subtract it inside the parenthesis. $(x^2 + 8x) - 7 = (x^2 + 8x + 16 - 16) - 7$<br /><br />## Step 3: Rewrite the perfect square trinomial<br />### The expression $x^2 + 8x + 16$ is a perfect square trinomial and can be factored as $(x+4)^2$. So, $(x^2 + 8x + 16 - 16) - 7 = (x+4)^2 - 16 - 7$<br /><br />## Step 4: Simplify the constant terms<br />### Combine the constant terms: $-16 - 7 = -23$. Thus, $(x+4)^2 - 16 - 7 = (x+4)^2 - 23$.