Chapter 9, Problem 1PFA

To determine

To select from the options, an equation that best models the data in the table

Answer to Problem 1PFA

Option D. $y=x^2-8x+15$

Explanation of Solution

Given information :

Option A. $y=2x-1$

Option B. $y=-2x+7$

Option C. $y=x^2+8x+15$

Option D. $y=x^2-8x+15$

Ordered pairs provided in the table:-

  $\begin{array}{l}(2,3)\\ (3,0)\\ (4,-1)\\ (5,0)\\ (6,3)\end{array}$

Any given equation of the form ( $y=a{x}^2+bx+c$ ) may pass through a certain point $(x,y)$ on the graph and this can be verified by putting the values of x and y in the equation provided. Therefore, we input ordered pairs in the options provided to check if they hold true.

Option A. $y=2x-1$

Substituting $(2,3)$ in the equation,

  $3=2\times 2-1$

Which holds true and it can be said that the equation does pass through $(2,3)$ .

Substituting $(3,0)$ in the equation,

  $0=2\times 3-1$

Which does not hold true and it can be said that the equation does not pass through $(3,0)$ .

Therefore, option A. $y=2x-1$ is rejected.

Option B. $y=-2x+7$

Substituting $(2,3)$ in the equation,

  $3=-2\times 2+7$

Which holds true and it can be said that the equation does pass through $(2,3)$ .

Substituting $(3,0)$ in the equation,

  $0=-2\times 3+7$

Which does not hold true and it can be said that the equation does not pass through $(3,0)$ .

Therefore, option A. $y=-2x+7$ is rejected.

Option C. $y=x^2+8x+15$

Substituting $(2,3)$ in the equation,

  $3=2^2+8\times 2+15$

Which does not hold true and it can be said that the equation does not pass through $(2,3)$ .

Therefore, option A. $y=x^2+8x+15$ is rejected.

Option D. $y=x^2-8x+15$

Substituting $(2,3)$ in the equation,

  $3=2^2-8\times 2+15$

Which holds true and it can be said that the equation does pass through $(2,3)$ .

Substituting $(3,0)$ in the equation,

  $0=3^2-8\times 3+15$

Which holds true and it can be said that the equation does pass through $(3,0)$ .

Substituting $(4,-1)$ in the equation,

  $-1=4^2-8\times 4+15$

Which holds true and it can be said that the equation does pass through $(4,-1)$ .

Similarly, it is seen that when ordered pairs are substituted in the equation it holds true for all ordered pairs in the table.

Therefore, Option D. $y=x^2-8x+15$ is selected as equation that best models the data given.