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How to write the formula for a parabola given the focus and vertex and the origin

4,646 views · Published 4 June 2014 · 3:10 · Indexed 20 September 2026

Channel: Brian McLogan · 2014 · Education

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Learn how to write the equation of a parabola given the vertex and the focus. A parabola is the shape of the graph of a quadratic equation. A parabola can open up or down (if x is squared) or open left or right (if y is squared). Recall that the focus and the vertex of a parabola are on the same line of symmetry.

When given the focus and the vertex of a parabola, recall that the focus of a parabola is inside the parabola. This enables us to identify the direction which the required parabola opens. We also need to identify the value of p, which is the distance between the vertex and the focus. p is negative when the parabola opens down or left and is positive when the parabola opens right or up.

Once we identify the direction and the value of p, we can use the equation of parabola given by (y - k)^2 = 4p(x - h) for parabolas that opens up or down and (x - h)^2 = 4p(y - k) for parabolas that opens left or right
#conicsections #parabolaconicsections

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