Chapter 4.7, Problem 1AGP

To determine

To write: the function in vertex form.

Answer to Problem 1AGP

The vertex form is $y={\left(x+2\right)}^2+2$ .

Explanation of Solution

Given information:

The function mentioned is $y=x^2+4x+6$ .

Formula:

For vertex form of quadratic equation we will use $y={\left(x-h\right)}^2+k$ where $\left(h,k\right)$ is the vertex.

Calculation:

Consider the quadratic equation $y=x^2+4x+6$ .

Recall that for vertex form of quadratic equation we will use $y={\left(x-h\right)}^2+k$ where $\left(h,k\right)$ is the vertex.

Therefore

  $\begin{array}{l}y=x^2+4x+6\Rightarrow y=\left(x^2+2*x*2+4-4+6\right)\\ \Rightarrow y=\left({\left(x+2\right)}^2+2\right)\Rightarrow y={\left(x+2\right)}^2+2.\end{array}$

Therefore the vertex form of the quadratic equation $y=x^2+4x+6$ is $y={\left(x+2\right)}^2+2$ .