Chapter 4.7, Problem 8PPS

To determine

To write: the function in vertex form.

Answer to Problem 8PPS

The vertex form is $y={\left(x+\frac{9}{2}\right)}^2-\frac{49}{4}$ .

Explanation of Solution

Given information:

The function mentioned is $y=x^2+9x+8$ .

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 $y=x^2+9x+8$ .

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

  $\begin{array}{l}y=x^2+9x+8\Rightarrow y=x^2+2*x*\frac{9}{2}+\frac{9^2}{2^2}-\frac{9^2}{2^2}+8\Rightarrow y={\left(x+\frac{9}{2}\right)}^2+8-\frac{81}{4}\\ \Rightarrow y={\left(x+\frac{9}{2}\right)}^2-\frac{49}{4}.\end{array}$

Therefore the vertex form of the quadratic equation $y=x^2+9x+8$ is $y={\left(x+\frac{9}{2}\right)}^2-\frac{49}{4}$ .