Chapter ISG, Problem 9.2.11P

To determine

To write: An equation for given graph using transformations.

Answer to Problem 9.2.11P

Equation is $y=-{(x+1)}^2+3$ .

Explanation of Solution

Given information: A relevant graph is given.

Calculation:

Considering the parent function quadratic function $f(x)=x^2$ and applying transformations on it:

Firstly, the function is reflected across the $x-axis$ ,

  $\begin{array}{l}j(x)=-f(x)\\ \\ j(x)=-x^2\end{array}$

Then the function is translated $3$ units up,

  $\begin{array}{l}k(x)=j(x)+3\\ \\ k(x)=-x^2+3\end{array}$

At last, function is translated $1$ unit to the left,

  $\begin{array}{l}h(x)=k(x+1)\\ \\ $ h(x)=-{(x+1)}^2+3$\end{array}$

Thus, equation is $y=-{(x+1)}^2+3$ .