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Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equation in standard form. [Hint: Vertex form: y - k = a(x - h)2]

User Andressa
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PART A

The equation of the parabola in vertex form is given by the formula,


y - k = a {(x - h)}^(2)

where


(h,k)=(1,-2)

is the vertex of the parabola.

We substitute these values to obtain,



y + 2 = a {(x - 1)}^(2)

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.



6 + 2 = a {(3 - 1)}^(2)



8= a {(2)}^(2)



8=4a



a = 2
Hence the equation of the parabola in vertex form is



y + 2 = 2 {(x - 1)}^(2)


PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.


y + 2 = 2{(x - 1)}^(2)

This implies that


y + 2 = 2(x - 1)(x - 1)


We expand to obtain,



y + 2 = 2( {x}^(2) - 2x + 1)


This will give us,



y + 2 = 2 {x}^(2) - 4x + 2



y = {x}^(2) - 4x

This equation is now in the form,


y = a {x}^(2) + bx + c
where


a=1,b=-4,c=0

This is the standard form
User Mahesh Samudra
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