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Write the equation in vertex form for the parabola with vertex (0,−2)(0,-2) and focus (0,3)(0,3).\newlineSimplify any fractions.\newline______

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Q. Write the equation in vertex form for the parabola with vertex (0,−2)(0,-2) and focus (0,3)(0,3).\newlineSimplify any fractions.\newline______
  1. Identify Direction: Identify the direction of the parabola.\newlineSince the focus is above the vertex, the parabola opens upwards.
  2. Find Distance: Find the distance between the vertex and the focus to determine the value of aa.\newlineDistance = ∣3−(−2)∣=5|3 - (-2)| = 5
  3. Calculate 'a': Calculate the value of 'a' using the distance. a=14×5=120a = \frac{1}{4 \times 5} = \frac{1}{20}
  4. Write Vertex Form: Write the vertex form of the parabola using the vertex (h,k)=(0,−2)(h,k) = (0,-2) and the value of ′a′'a'. \newliney=a(x−h)2+ky = a(x-h)^2 + k\newliney=120(x−0)2−2y = \frac{1}{20}(x-0)^2 - 2\newliney=120x2−2y = \frac{1}{20}x^2 - 2

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