Question

Which is the equation of the parabola?

Answer 1

Answer: $y=-\dfrac{1}{8}(x - 2)^2 - 3$

Step-by-step explanation:

The vertex form of a parabola is: y = a(x - h)² + k    where

• (h, k) is the vertex
• $a=\dfrac{1}{4p}$  

NOTE: p is the distance from the vertex to the focus

The vertex (h, k) is (2, -3)

$p=-2\quad \implies\quad a = \dfrac{1}{4(-2)}=-\dfrac{1}{8}$

Insert those values into the vertex formula to get:

$y=-\dfrac{1}{8}(x - 2)^2 - 3$