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Write the equation in vertex form for the parabola with vertex (0,7)(0,7) and directrix y=6y = 6.\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 directrix y=6y = 6.\newlineSimplify any fractions.\newline______
  1. Identify orientation: Identify the orientation of the parabola.\newlineSince the directrix is horizontal y=6y = 6, the parabola is vertical.
  2. Determine opening direction: Determine the direction the parabola opens. The vertex (0,7)(0,7) is above the directrix y=6y = 6, so the parabola opens upwards.
  3. Find distance to directrix: Find the distance between the vertex and the directrix.\newlineDistance = ∣7−6∣=1|7 - 6| = 1.
  4. Calculate value of 'a': Calculate the value of 'a' using the distance.\newlineThe distance is equal to 14a\frac{1}{4a}, so a=14a = \frac{1}{4}.
  5. Write vertex form: Write the vertex form of the parabola using the vertex (h,k)=(0,7)(h,k) = (0,7) and the value of ′a′'a'. The vertex form is y=a(x−h)2+ky = a(x-h)^2 + k. Substitute a=14a = \frac{1}{4}, h=0h = 0, and k=7k = 7. y=14(x−0)2+7y = \frac{1}{4}(x-0)^2 + 7.
  6. Simplify equation: Simplify the equation. y=14x2+7y = \frac{1}{4}x^2 + 7.

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