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What is the focus of the parabola y=4x2y = 4x^2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=4x2y = 4x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Identify Orientation: Identify the orientation of the parabola.\newlineSince the equation is y=4x2y = 4x^2, it's a vertical parabola.
  2. Write in Vertex Form: Write the equation in vertex form to find aa, hh, and kk. The equation y=4x2y = 4x^2 is already in the form y=a(x−h)2+ky = a(x - h)^2 + k with a=4a = 4, h=0h = 0, and k=0k = 0.
  3. Calculate Value of p: Calculate the value of p using the formula p=14ap = \frac{1}{4a}. \newlinep=14×4p = \frac{1}{4\times 4}\newlinep=116p = \frac{1}{16}
  4. Find the Focus: Find the focus using the values of hh, kk, and pp. The focus is at (h,k+p)(h, k + p) which is (0,0+116)(0, 0 + \frac{1}{16}).

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