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

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Q. What is the focus of the parabola y=2x2y = 2x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Vertical Parabola: y=2x2y = 2x^2 is a vertical parabola.
  2. Standard Form: The standard form is y=a(x−h)2+ky = a(x - h)^2 + k, so a=2a = 2, h=0h = 0, and k=0k = 0.
  3. Calculate pp: To find the focus, use p=14ap = \frac{1}{4a}, so p=14×2p = \frac{1}{4 \times 2}.
  4. Find Focus: Calculate pp: p=18p = \frac{1}{8}.
  5. Calculate Coordinates: The focus is at (h,k+p)(h, k + p), so it's (0, 0 + rac{1}{8}).
  6. Final Focus: The focus of the parabola is (0, rac{1}{8}).

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