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What is the focus of the parabola y=−3x2y = -3x^2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=−3x2y = -3x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Identify Parabola Orientation: Identify the orientation of the parabola.\newlineSince the equation is y=−3x2y = -3x^2, it's a vertical parabola.
  2. Find Values of aa, hh, kk: Find the values of aa, hh, and kk. The equation y=−3x2y = -3x^2 can be rewritten as y=−3(x−0)2+0y = -3(x - 0)^2 + 0. So, a=−3a = -3, h=0h = 0, and hh00.
  3. Calculate Value of p: Calculate the value of pp using the formula p=14ap = \frac{1}{4a}.p=14(−3)p = \frac{1}{4(-3)}p=−112p = -\frac{1}{12}
  4. Determine Parabola Focus: Determine the focus of the parabola using the values of hh, kk, and pp. The focus is at (h,k+p)(h, k + p). So, the focus is at (0,0+(−112))(0, 0 + (-\frac{1}{12})).
  5. Write Focus Coordinates: Write the coordinates of the focus.\newlineThe focus of the parabola is (0,−112)(0, -\frac{1}{12}).

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