Okay so the question is:
$x^2-10x+18$ has to be written in the form $(x-a)^2+b$ and I have to provide the values of $a$ and $b$.
I worked out that $a= -5$ and $b= -7$.
On the video I am watching, he states that $a=+5$ not $-5$, and $b= -7$. I understand why he got $b = -7$, but how is $a = +5$? when clearly it states in the brackets $(x-5)^2$.
On
You have $(x-5)^2-7=(x-a)^2+b$ so that $$-5=-a \text { therefore } a=5$$$$-7=b\text { therefore } b=-7$$
Until you get used to the signs in these expressions it is worth taking a little extra care and writing the parallel expressions next to one another (or one below the other).
On
Think of $(x-a)^2+b$ as "($x$ minus a number)$^2$ plus another number" and not just as a template to plug and chug.
What is required in parentheses is "$x$ minus a number", so you need to always write the minus sign, whether the constant $a$ is positive or negative.
for example the following $$(x-7)^2+3$$ $$(x+9)^2+8$$ $$(x+11)^2-4$$ should be written as $$(x-(7))^2+(3)$$ $$(x-(-9))^2+(8)$$ $$(x-(-11))^2+(-4)$$ Notice how the $a$ is subtracted and the $b$ is added, otherwise the expression wouldn't be in the form $(x-a)^2+b$.
Because you shall produce an expression $(x-a)^2+b$, not $(x+a)^2+b$.