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What is the focus of the parabola y=−5x2y = -5x^2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=−5x2y = -5x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Identify vertex form: Identify the vertex form of the parabola. \newliney=−5x2y = -5x^2 can be written as y=−5(x−0)2+0y = -5(x - 0)^2 + 0, where a=−5a = -5, h=0h = 0, and k=0k = 0.
  2. Calculate p value: Calculate the value of pp using the formula p=14ap = \frac{1}{4a}.p=14(−5)p = \frac{1}{4(-5)}p=−120p = -\frac{1}{20}
  3. Find focus: Find the focus of the parabola using the vertex (h,k)(h, k) and the value of pp. The focus is at (h,k+p)(h, k + p). Focus = (0,0+(−120))(0, 0 + (-\frac{1}{20})) Focus = (0,−120)(0, -\frac{1}{20})

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