Chapter 9, Problem 8PFA

To determine

To select from options the equation that correctly describes the graph.

Answer to Problem 8PFA

Option D. $x^2-6x=-9$

Explanation of Solution

Given information :

Option A. $x^2+6x=9$

Option B. $x^2+6x=-9$

Option C. $x^2-6x=9$

Option D. $x^2-6x=-9$

From the graph shown, it is evident that the vertex is at $(3,0)$ .

Option A. $x^2+6x=9$

  $x=3$ is substituted in the equation shown below corresponding to the vertex.

Then, the expression $x^2+6x-9$ should be equal to 0

  $3^2+6\times 3-9=0$

The above equation does not hold true, hence option A. is rejected.

Option B. $x^2+6x=-9$

  $x=3$ is substituted in the equation shown below corresponding to the vertex.

Then, the expression $x^2+6x+9$ should be equal to 0

  $3^2+6\times 3+9=0$

The above equation does not hold true, hence option B. is rejected.

Option C. $x^2-6x=9$

  $x=3$ is substituted in the equation shown below corresponding to the vertex.

Then, the expression $x^2-6x-9$ should be equal to 0

  $3^2-6\times 3-9=0$

The above equation does not hold true, hence option C. is rejected.

Option D. $x^2-6x=-9$

  $x=3$ is substituted in the equation shown below corresponding to the vertex.

Then, the expression $x^2-6x+9$ should be equal to 0

  $3^2-6\times 3+9=0$

The above equation does hold true, hence option D. is selected as the correct answer.