Chapter 9.2, Problem 44HP

To determine

To explain: Explain whether all quadratic functions that are reflected across the $y-\mathrm{axis}$ produce the same graph.

Answer to Problem 44HP

No, all quadratic functions are not reflected across the $y-\mathrm{axis}$ to produce the same graph.

Explanation of Solution

Given information: The given problem is about all quadratic functions that are reflected across the $y-\mathrm{axis}$ produce the same graph.

Calculation: The all quadratic functions that are reflected across the $y-\mathrm{axis}$ produce the same graph.

All quadratic equations that are reflected across $y-\mathrm{axis}$ produce the same graph. If the quadratic is of the form $g(x)=a{x}^2+k$ ,then reflecting across the $y-\mathrm{axis}$ does produce the same graph since the reflection is $g(-x)=a{(-x)}^2+k=a{x}^2+k$ .If the quadratic equations is of the form $h(x)=a{(x-h)}^2+k$ ,the reflected graph will not be the same since

  $\begin{array}{}$ h(-x)=a{(-x-h)}^2+k$$ h(-x)={(-1)}^{2}a{(x+h)}^2+k$$ h(-x)=a{(x+h)}^2+k\ne h(x).$\end{array}$

Thus, the answer is No.