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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 Parabola Type: y=−4x2y = -4x^2 is a vertical parabola, so we use the formula y=a(x−h)2+ky = a(x - h)^2 + k to find the focus.
  2. Find Parameters: Identify aa, hh, and kk. Here, a=−4a = -4, h=0h = 0, and k=0k = 0.
  3. Calculate pp: Find the value of pp using p=14ap = \frac{1}{4a}. So, p=14(−4)=1−16=−116p = \frac{1}{4(-4)} = \frac{1}{-16} = -\frac{1}{16}.
  4. Determine Focus: The focus of a vertical parabola is (h,k+p)(h, k + p). So, the focus is (0,0+(−116))(0, 0 + (-\frac{1}{16})).
  5. Final Result: Therefore, the focus is (0, - rac{1}{16}).

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