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Write the equation in vertex form for the parabola with vertex (0,0)(0,0) and directrix y=−10y = -10.\newlineSimplify any fractions.\newline______

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Q. Write the equation in vertex form for the parabola with vertex (0,0)(0,0) and directrix y=−10y = -10.\newlineSimplify any fractions.\newline______
  1. Identify Orientation: Identify the orientation of the parabola based on the directrix.\newlineSince the directrix is y=−10y = -10, which is horizontal, the parabola is vertical.
  2. Determine Opening Direction: Determine the direction the parabola opens. The vertex (0,0)(0,0) is above the directrix y=−10y = -10, so the parabola opens upwards.
  3. Calculate Distance: Calculate the distance between the vertex and the directrix.\newlineThe distance is ∣0−(−10)∣=10|0 - (-10)| = 10.
  4. Find Value of 'a': Find the value of 'a' using the distance.\newlineThe distance is equal to 14a\frac{1}{4a}, so 10=14a10 = \frac{1}{4a}.\newlineSolving for 'a' gives a=140a = \frac{1}{40}.

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