Question

What are the coordinates of the focus of the parabola?

y=−18x2−2x−4


A (−8, 6)

B (−8, 2)

C (8, 6)

D (8, 2)

Answer 1

Explanation:

To find the coordinates of the focus of a parabola in the general form y = ax^2 + bx + c, you can use the formula (h, k) where h = -b/(2a) and k = (4ac - b^2)/(4a).

In the given equation y = -18x^2 - 2x - 4, we can identify that a = -18, b = -2, and c = -4. Plugging these values into the formulas, we get:

h = -(-2)/(2*(-18)) = 1/18

k = (4*(-18)*(-4) - (-2)^2)/(4*(-18)) = -71/9

Therefore, the focus of the parabola is (1/18, -71/9).

None of the given answer options match the coordinates of the focus calculated, so none of the options (A, B, C, D) are correct.