How to find the equation of a parabola in standard form as well as the ordered pair for the focus point and the equation of the directrix

Question

The vertex of the parabola is (-7.99,5) and a point on it is (-9,4) and it opens downward...and that's all I know

Answer 1

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Answer 2

Given: Vertex of parabola is (-7.99, 5)

opens downward,

and a point on the parabola (-9,4)

Find the equation of the parabola.

SOLUTION:

y = a(x - h)^2 + k Vertex at (h,k)

y = -(4p)(x + 7.99)^2 + 5

Use the given point to find p,

4 = -(4p)(-9 + 7.99)^2 + 5

4 = -(4p)(-1.01)^2 + 5

4 = -(4p)(1.0201) + 5

-1 = -(4p)(1.0201)

1 = p*(4.0804)

p = 1/(4.0804)

p = .24507401

Directrix:

y = 5 + p

y = 5.2450701

Focus:

(-7.99, 5 - p ) = (-7.99, 4.754926 )

Convert to Standard Form:

y = -(4p)(x + 7.99)^2 + 5

y = -(4)(.24507401)(x + 7.99)^2 + 5

y = -(.98029605)(x + 7.99)^2 + 5

y = -(.98029605)*[ x^2 + 15.98x + 63.8401 ] + 5

y = -(.980296)x^2 - (15.6651)x - 62.582198 + 5

y = -(.980296)x^2 - (15.6651)x - 57.582198 Standard Form