Answer: [tex]y=-\dfrac{1}{8}(x - 2)^2 - 3[/tex]
Step-by-step explanation:
The vertex form of a parabola is: y = a(x - h)² + k where
- (h, k) is the vertex
- [tex]a=\dfrac{1}{4p}[/tex]
NOTE: p is the distance from the vertex to the focus
The vertex (h, k) is (2, -3)
[tex]p=-2\quad \implies\quad a = \dfrac{1}{4(-2)}=-\dfrac{1}{8}[/tex]
Insert those values into the vertex formula to get:
[tex]y=-\dfrac{1}{8}(x - 2)^2 - 3[/tex]
