Answer to Question #270008 in Analytic Geometry for Angel Nodado

Question

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

Answer 1

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

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

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

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

Or

$$y=-x^2+6x-5$$