Chapter 9.2, Problem 47PFA

To determine

To find the equation of the second graph based on the parent graph.

Answer to Problem 47PFA

C. The equation for the second graph is $f\left(x\right)=x^2+6x+7$ .

Explanation of Solution

Given information :

The parent graph is given by the function $f\left(x\right)=x^2$ .

Formula used :

To derive at the function of the shifted parabola left, along the x-axis, add the numeric value of the point that graph is shifted left inside the $x^2$ component.

To derive at the function of the shifted parabola downwards, along the y-axis, subtract the numeric value of the point in the parent function. This should be giving the function of the new graph.

Calculation :

Since the graph is shifted 3 units to the left, add 3 within $x^2$ .

  $f\left(x\right)={\left(x+3\right)}^2$

Since the graph is shifted 2 units downwards, subtract 2 from the resultant equation.

  $f\left(x\right)={\left(x+3\right)}^2-2$

On Simplifying this,

  $=x^2+6x+9-2$

This gives the final equation of the graph.

  $f\left(x\right)=x^2+6x+7$

Hence the equation of the shifted graph is option C.