Answer to Question #270008 in Analytic Geometry for Angel Nodado

Question #270008

Use the information provided to write the standard form equation of the parabola.Vertex:(3,4) Focus:(3 ¹⁵/⁴)


1
Expert's answer
2021-11-24T10:06:32-0500

If you have the equation of a parabola in vertex form y=a(xh)2+k,y=a(x−h)^2+k, then the vertex is at (h,k)(h,k) and the focus is (h,k+1/(4a))(h, k+1/(4a))

Vertex: (3,4).(3,4). Then h=3,k=4.h=3, k=4.

Focus: (3,15/4).(3, 15/4). Then 4+1/(4a)=15/4=>a=14+1/(4a)=15/4=>a=-1


The equation of a parabola in vertex form is y4=(x3)2.y-4=-(x-3)^2.

Or

y=x2+6x5y=-x^2+6x-5


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