Question

In the parabola,

y=3x^2+12x+11, the focus is located at a distance p>0 from the vertex. Then
p=
a. 3
b. 1/3
c. 12
d. 1/12
e. None of the above

Answer 1

The focus of the parabola y=3x^2+12x+11 is located at a distance of 1/12 units from the vertex.

Step-by-step explanation:

The equation y = 3x^2 + 12x + 11 represents a parabola. To find the focus of the parabola, we first need to convert the equation into the standard form y = a(x - h)^2 + k. Comparing the given equation with the standard form, we can see that a = 3, h = -12/6 = -2, and k = 11 - (3(-12/6)^2) = 5.

The vertex of the parabola is given by (h, k), which in this case is (-2, 5). The focus of the parabola is located at a distance p = 1/(4a) units from the vertex. Substituting the value of a, we get p = 1/(4(3)) = 1/12.

Therefore, the correct answer is d. 1/12.