Chapter 1.4, Problem 2Q

Solution

To graph: the given function.

  

Given:

  $y=2x^2+8x+15$ .

Concept used:

The x-coordinate of the vertex of the graph of $y=a{x}^2+bx+c$ is $x=-\frac{b}{2a}$ .

Calculation:

Comparing $y=2x^2+8x+15$ with $y=a{x}^2+bx+c$ , it follows that:

  $a=2,b=8,c=15$ .

Now the x -coordinate of the vertex is,

  $\begin{array}{l}x=-\frac{8}{2\left(2\right)}\\ x=-2\end{array}$

Now when $x=-2$ ,

  $\begin{array}{c}y=2{\left(-2\right)}^2+8\left(-2\right)+15\\ =7\end{array}$

Therefore, the vertex is at $\left(-2,7\right)$ .

Now the graph is,