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Write the equation in vertex form for the parabola with vertex (0,7)(0,7) and focus (0,10)(0,10).\newlineSimplify any fractions.\newline______

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Q. Write the equation in vertex form for the parabola with vertex (0,7)(0,7) and focus (0,10)(0,10).\newlineSimplify any fractions.\newline______
  1. Identify Vertex Form: Identify the vertex form of a vertical parabola.\newlineVertex form: y=a(x−h)2+ky = a(x-h)^2 + k
  2. Given Vertex and Focus: Given vertex (h,k)=(0,7)(h,k) = (0,7) and focus (0,10)(0,10). Since the focus is above the vertex, the parabola opens upwards.
  3. Calculate Distance for 'a': Calculate the distance between the vertex and focus to find the value of 'a'.\newlineDistance p=∣10−7∣=3p = |10 - 7| = 3
  4. Calculate 'a' Value: The value of 'a' is 14p\frac{1}{4p}. \newlinea=14×3a = \frac{1}{4\times3}\newlinea=112a = \frac{1}{12}
  5. Substitute Values into Equation: Substitute aa, hh, and kk into the vertex form equation.y=112(x−0)2+7y = \frac{1}{12}(x-0)^2 + 7y=112x2+7y = \frac{1}{12}x^2 + 7

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