Question

Find an equation of a parabola that satisfies the given conditions. Vertex (0,0), focus (-2,0).

a) y = x²
b) y = x² + 2
c) y = x² - 2
d) y = x² - 4

Answer 1

The equation of a parabola with vertex (0,0) and focus (-2,0) is y = (1/8)x².

Step-by-step explanation:

The equation of a parabola with vertex (0,0) and focus (-2,0) can be found using the formula y = a(x-h)² + k, where (h,k) is the vertex. For this parabola, the vertex is (0,0), so we have y = ax².

To find the value of a, we can use the distance formula from the focus to a point on the parabola, which is given by a = 1/4f, where f is the distance from the vertex to the focus. In this case, f = 2, so a = 1/4(2) = 1/8. Therefore, the equation of the parabola is y = (1/8)x².