Answer
$(x+1)^2=\frac{1}{2}y$
Work Step by Step
Step 1. Identify the given quantities: parabola vertex $V(-1,0)$, horizontal axis of symmetry, y-intercept $(0,2)$
Step 2. With the vertex and horizontal axis of symmetry, we can assume the equation as $(x+1)^2=cy$ (where $c$ is a constant).
Step 3. Plug-in the coordinates of the y-intercept to get $(0+1)^2=2c$ thus $c=\frac{1}{2}$
Step 4. The equation for the parabola is $(x+1)^2=\frac{1}{2}y$
