Question

I would greatly appreciate if someone could explain this to me!

Answer 1

Remember that, in general, a quadratic equation can be written as:

$ax^2+bx+c$

In our problem, we already have the values of a and b, c is the missing value. When this happens, that a and b are given, the value of c is equal to:

$c=(\frac{b}{2})^2$

Therefore, the missing value in the problem is:

$\begin{gathered} b=-2 \\ \Rightarrow c=(-\frac{2}{2})^2=(-1)^2=1 \\ \Rightarrow c=1 \end{gathered}$

Thus, the answer is 1

We can easily verify that this answer is correct as follows:

$x^2-2x+1=(x-1)(x-1)=(x-1)^2$