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What is the correct standard form of the equation of the parabola? Be sure to show each step of your work of how you got to the equation

What Is The Correct Standard Form Of The Equation Of The Parabola Be Sure To Show Each Step Of Your Work Of How You Got To The Equation class=

Sagot :

Answer:

[tex](x+3)^2=4(y-3)[/tex]

Step-by-step explanation:

Parabolas

In conic sections, the standard form of a parabola with a vertex at (h, k) is

                                      [tex](x-h)^2=4p(y-k)[/tex] ,

when the parabola is parallel to the y-axis (opens up/down);

                                      [tex](y-k)^2=4p(x-h)[/tex],

when the parabola is parallel to the x-axis (opens left/right);

The distance between the vertex and the directrix (line) is the same as the distance between the vertex and the focus point, this distance is represented by "p".

[tex]\hrulefill[/tex]

Solving the Problem

Determine Which Standard Form to Use

The parabola opens downwards, so we use [tex](x-h)^2=4p(y-k)[/tex].

Identifying the Parabola's Equation

The parabola has a vertex at (-3, 3), so h = -3 and k = 3.

The distance between the vertex and focus point (-3, 2) is 1, so p = 1.

Putting it all together,

                             [tex](x-(-3))^2=4(1)(y-3)[/tex]

                                  [tex](x+3)^2=4(y-3)[/tex].

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