Question

practice putting a standard form function into vertex form. show all work. 6. y = x² - 6x + 2 vertex form. vertex

Explanation:

Step1: Identify coefficients

For the quadratic function $y = x^{2}-6x + 2$, where $a = 1$, $b=-6$, $c = 2$.

Step2: Complete the square

\[

$$\begin{align*} y&=x^{2}-6x + 2\\ y&=(x^{2}-6x)+2\\ y&=(x^{2}-6x + 9-9)+2\\ y&=(x - 3)^{2}-9 + 2 \end{align*}$$

\]

Step3: Simplify the expression

\[y=(x - 3)^{2}-7\]
The vertex - form of a quadratic function is $y=a(x - h)^{2}+k$, where $(h,k)$ is the vertex of the parabola. Here $h = 3$ and $k=-7$.

Answer:

Vertex form: $y=(x - 3)^{2}-7$
Vertex: $(3,-7)$