Question

put the equation $y = x^{2}-12x + 35$ into the form $y=(x - h)^{2}+k$. answer: $y=$

Explanation:

Step1: Complete the square for the $x$ - terms

For the quadratic expression $x^{2}-12x$, the coefficient of $x$ is $- 12$. Half of this coefficient is $\frac{-12}{2}=-6$, and its square is $(-6)^{2} = 36$.
We rewrite $y=x^{2}-12x + 35$ as $y=(x^{2}-12x+36)-36 + 35$.

Step2: Simplify the expression

Using the perfect - square formula $(a - b)^2=a^{2}-2ab + b^{2}$, where $a = x$ and $b = 6$, we have $x^{2}-12x + 36=(x - 6)^{2}$.
So $y=(x - 6)^{2}-1$.

Answer:

$y=(x - 6)^{2}-1$