Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.

The focus of a parabola is (0Ė-2) . The directrix is the line y = 0. What is the equation of the parabola in vertex form?
In the equation y = (2
The vertex of the parabola is the point (0
The equation of this parabola in vertex form is y=
-
k)² + h, the value of p is 0.5
-0.5
-1/2
).
²-1

Answer 1

The focus of a parabola is (0, -2), and the directrix is the line y = 0. Given this information, we can find the equation of the parabola in vertex form.

The vertex form of the equation for a parabola with its vertex at the point (h, k) and the focus at (h, k + p) or (h, k - p) is:

(y - k)² = 4p(x - h)

In this case, the vertex is (h, k) = (0, -1), and the focus is (h, k + p) = (0, -2). So, p = -1.

Now, we can plug these values into the vertex form equation:

(y - (-1))² = 4(-1)(x - 0)

Simplify:

(y + 1)² = -4x

So, the equation of the parabola in vertex form is:

y = (x²) - 1