Chapter 8.5, Problem 48E

To determine

To write the quadratic function in standard form whose graph satisfies the given conditions.

Answer to Problem 48E

The quadratic function in standard form is $x^2+7x+10=0$ .

Explanation of Solution

Given information:

  $x-\text{intersecpts:}-2\text{and }-\text{5}\text{.}$

Calculation:

  $x-\text{intersecpts}\text{are}-2\text{and }-5.$

So,

  $\begin{array}{c}x=-2\text{,}x=-5\\ x+2=0\text{,}x+5=0\end{array}$

Now, the cubic function will be,

  $\begin{array}{c}\left(x+2\right)\left(x+5\right)=0\\ x\left(x+5\right)+2\left(x+5\right)=0\\ x^2+5x+2x+10=0\\ x^2+7x+10=0\end{array}$

The quadratic function in standard form is $x^2+7x+10=0$ .