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Write the equation of the parabola in vertex form.
vertex (3,2), point (2,-4)
f(x)=

Write The Equation Of The Parabola In Vertex Form Vertex 32 Point 24 Fx class=

Sagot :

The equation of the parabola in vertex form

[tex]y=-6(x-3)^2+2[/tex]

Given :

vertex (3,2), point (2,-4)

The vertex form of parabola is [tex]y=a(x-h)^2+k[/tex]

Where (h,k) is the vertex

Given vertex is (3,2). so, h=3 and k=2

Replace it in the equation

[tex]y=a(x-3)^2+2[/tex]

Now we find out the value of 'a' using the given point (2,-4)

Point (2,-4) is (x,y)

x=-2  and y=-4

Replace it in the equation we got to find out 'a'

[tex]y=a(x-3)^2+2\\-4=a(2-3)^2+2\\-4=a(1)+2\\-4=a+2\\-4-2=a\\a=-6[/tex]

the equation of the parabola in vertex form

[tex]y=-6(x-3)^2+2[/tex]

Learn more : brainly.com/question/9030390

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