How to find the equation of a parabola given the vertex and directrix

Equation of a horizontal parabola: The equation of a horizontal parabola is (y − k)2 = 4p(x − h), where (h, k) is the vertex, and | p | is half the distance between the focus and the directrix

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Conics: Parabolas: Finding the Equation from Information

To find the vertex (h, k) of a parabola that is in intercept form y = a(x - p) (x - q): Use h = (p + q) / 2 for finding h; Substitute x = h in the equation of parabola to find k. What are the Properties

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How do you find an equation of the parabola with vertex

If a parabola has a horizontal axis, the standard form of the equation of the parabola is this: (y - k)2 = 4p (x - h), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h + p, k). The directrix is the line x = h - p.
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Finding Equation of Parabola Given Vertex and Directrix

Finding the Focus, Vertex, and Directrix of a parabola – Example: Find vertex and focus of this parabola: \(y=3x^2+6x\) Solution: The Parabola given parameters are: \(a=3, b=6

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