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Precalculus · G-GPE

Parabola — Standard Form and Focus-Directrix

Parabola with vertex (h,k) opening up: (x−h)² = 4p(y−k), focus at (h, k+p), directrix y = k−p.

PrecalculusCommon Core HSG-GPE.A.2G-GPEVerified correct ✓

Worked examples

A parabola with vertex (4, -3) opens upward with p = 0.5. Find the y-value of the directrix (y = k − p).
Answer: -3.5
A parabola has vertex (-4, -4) and a = 1. Using (x + 4)² = 4p(y + 4), find p and then give the y-coordinate of the focus.
Answer: -3.75

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