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What is the focus of the parabola y=3x2y = 3x^2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=3x2y = 3x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Parabola Direction: y=3x2y = 3x^2 is a vertical parabola, so it opens upwards.
  2. Standard Form: The standard form of a parabola is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex.
  3. Vertex Coordinates: For y=3x2y = 3x^2, a=3a = 3, h=0h = 0, and k=0k = 0 because it's not shifted from the origin.
  4. Focus Formula: The focus of a parabola is (h,k+p)(h, k + p), where p=14ap = \frac{1}{4a}.
  5. Calculate pp: Calculate pp: p=14×3=112p = \frac{1}{4 \times 3} = \frac{1}{12}.
  6. Calculate Focus: Now plug in hh, kk, and pp to find the focus: (0,0+112)=(0,112)(0, 0 + \frac{1}{12}) = (0, \frac{1}{12}).

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