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Write the equation in vertex form for the parabola with vertex (0,4)(0,4) and focus (0,7)(0,7).\newlineSimplify any fractions.\newline______

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Q. Write the equation in vertex form for the parabola with vertex (0,4)(0,4) and focus (0,7)(0,7).\newlineSimplify any fractions.\newline______
  1. Identify Orientation: Identify the orientation of the parabola based on the vertex and focus.\newlineSince the vertex and focus have the same xx-coordinate, the parabola is vertical.
  2. Determine Opening Direction: Determine the direction the parabola opens.\newlineThe focus (0,7)(0,7) is above the vertex (0,4)(0,4), so the parabola opens upwards.
  3. Calculate Distance for 'a': Calculate the distance between the vertex and the focus to find the value of 'a'.\newlineDistance = ∣7−4∣=3|7 - 4| = 3\newlineThe value of 'a' is 14⋅3\frac{1}{4\cdot3} because the parabola opens upwards.
  4. Write Vertex Form: Write the vertex form of the equation using the vertex (h,k)=(0,4)(h,k) = (0,4) and the value of ′a′'a'. \newliney=a(x−h)2+ky = a(x-h)^2 + k\newliney=112(x−0)2+4y = \frac{1}{12}(x-0)^2 + 4\newliney=112x2+4y = \frac{1}{12}x^2 + 4

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