Find the vertex of the parabola associated with the quadratic function.

f(x)= -1/7x^2 - 2/11x + 1/121

(h,k)= What is the vertex of this quadratic function?

Hint: the x-coordinate of the vertex of a parabola y = ax^2 + bx + c is -b/2a.

F(x) = -x^2/7 - 2x/11 + 1/121,

h = -b/2a = (2/11) / (-2/7) = -7/11.

k = -(-7/11)^2/7 -2(-7/11)/11 + 1/121,
k = -(49/121*1/7 + 14/11/11 + 1/121,
k = -7/121 +14/121 + 1/121 = 8/121.

V(h,k) = V(-7/11,8/121).

y^2+4y+2x=0

To find the vertex of a quadratic function in the form f(x) = ax^2 + bx + c, we can use the formula x = -b/2a to find the x-coordinate of the vertex. Once we have the x-coordinate, we can substitute it back into the function to find the corresponding y-coordinate.

In the given quadratic function f(x) = -1/7x^2 - 2/11x + 1/121, we can identify a = -1/7, b = -2/11, and c = 1/121.

Using the formula x = -b/2a, we substitute the values of a and b:
x = -(-2/11) / (2 * (-1/7))
x = 2/11 / (-2/7)
x = (2/11) * (-7/2)
x = -7/11

Now we substitute this x-coordinate back into the original function to find the y-coordinate:
f(-7/11) = -1/7 * (-7/11)^2 - 2/11 * (-7/11) + 1/121
f(-7/11) = -1/7 * 49/121 - 14/121 + 1/121
f(-7/11) = -49/847 - 14/121 + 1/121
f(-7/11) = (-49 * 11) / (11 * 7 * 121) - (14 * 7) / (11 * 7 * 121) + 1 / (11 * 121)
f(-7/11) = -539 / 847 + 98 / 847 + 1 / 1331
f(-7/11) = (-539 + 98 + 1) / 847 * 1331
f(-7/11) = -440 / 847 * 1331
f(-7/11) = -440 / 112457.4

So, the vertex of the given quadratic function is approximately (h, k) = (-7/11, -440/112457.4)