Answer:
[tex]-\frac{1}{2} (x - 1)^2 + 1[/tex]
Explanation:
Since it is flipped and now extending to negative infinity, we make [tex]x^2[/tex] negative, so it is [tex]-x^2[/tex].
Lastly, there are a few shifts, it is shifted right once and up once.
To shift it right once, you would subtract a 1 from x directly: [tex]-(x - 1)^2[/tex]
To shift it up once, you would add 1 to the entire equation: [tex]-(x - 1)^2 + 1[/tex]
To account for the stretching, it would be: [tex]-\frac{1}{2} (x - 1)^2 + 1[/tex]
