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The equation of a parabola is 12y=(x-1)^2-48 identify the vertex , focus, and directrix of the parabola.

The equation of a parabola is 12y=(x-1)^2-48 identify the vertex , focus, and directrix of the parabola.
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Major Spinka DVM

Feb 20, 2025

the equation of a vertically opening parabola is(x - h)² = 4p(y - k)where (h, k) are the coordinates of the vertex and p is the distance of the focus and directrix from the vertex. If 4p is positive parabola opens up and if 4p is negative parabola opens downrearrange 12y = (x - 1)² - 48 into this form(x - 1)² = 12y + 48 (x - 1)² = 12( y + 4) ← in standard formVertex = (1, - 4 )4p = 12 ⇒ p = 3 ⇒ parabola opens upwardsthe focus is above the vertex and the directrix is below the vertex in a vertically opening up parabolaFocus = (1, - 4 + 3 ) = (1, - 1)Directrix has equation y = - 4 - 3 ⇒ y = - 7... Show More
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M
Major Spinka DVM

Feb 20, 2025

Vertex = (1,-4)Focus = (1, -1)Directix = y= -7Hope this helped... Show More
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