Question

write y = x^2 - 18x + 52 in vertex form.

Explanation:

Step1: Recall vertex - form formula

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. Given $y=x^{2}-18x + 52$, for a quadratic function $y=ax^{2}+bx + c$ ($a = 1$, $b=-18$, $c = 52$), we use the method of completing the square.

Step2: Complete the square for the $x$ - terms

First, take the coefficient of $x$, which is $b=-18$. Half of it is $\frac{b}{2}=\frac{-18}{2}=-9$. Then $(x - 9)^{2}=x^{2}-18x + 81$. We have $y=x^{2}-18x+52=(x^{2}-18x+81)-81 + 52$.

Step3: Simplify the expression

$y=(x - 9)^{2}-29$.

Answer:

$y=(x - 9)^{2}-29$