ANSWER
Josie did not make a mistake
Step-by-step explanation
The vertex form of a quadratic equation is given in the form:
![y=(x-h)^2\text{ + k}](https://img.qammunity.org/2023/formulas/mathematics/college/33kaa2s5bdr7l0pvi3l9bnh4konbjugbcv.png)
where (h, k) is the vertex
Jose rewrote the given equation to arrive at:
![y\text{ = (x - }2)^2\text{ - 8 }](https://img.qammunity.org/2023/formulas/mathematics/college/5wcw955byckmxx46admgqhsh186gb6qjbk.png)
And her vertex was (2, -8)
Comparing this with the general form written above, we see that every step taken and the final answer are correct.
Therefore, Josie did not make a mistake.