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What is the focus of the parabola y=−2x2−4y = -2x^2 - 4?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=−2x2−4y = -2x^2 - 4?\newlineSimplify any fractions.\newline(______,______)
  1. Identify vertex form: Identify the vertex form of the parabola.\newlineThe given equation y=−2x2−4y = -2x^2 - 4 is similar to y=a(x−h)2+ky = a(x - h)^2 + k.\newlineHere, a=−2a = -2, h=0h = 0, and k=−4k = -4.
  2. Calculate p value: Calculate the value of pp using the formula p=14ap = \frac{1}{4a}.p=14(−2)p = \frac{1}{4(-2)}p=−18p = -\frac{1}{8}
  3. Find focus: Find the focus of the parabola.\newlineThe focus is at (h,k+p)(h, k + p).\newlineSubstitute h=0h = 0, k=−4k = -4, and p=−18p = -\frac{1}{8}.\newlineFocus: (0,−4−18)(0, -4 - \frac{1}{8})\newlineFocus: (0,−338)(0, -\frac{33}{8})

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