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Drag each label to the correct location in the table.Match each attribute of the parabolic graph to its corresponding equation.Focus:Vertex: (-4,-3)Directrix: 1Vertex: (4,3)x=-2(y + 3)2 - 4x = 2(y - 3)2 + 4

Drag Each Label To The Correct Location In The TableMatch Each Attribute Of The Parabolic Graph To Its Corresponding EquationFocusVertex 43Directrix 1Vertex 43x class=

Sagot :

Given the parabolas:

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

You can identify that they are horizontal parabolas written in Vertex Form:

[tex]x=(y-k)^2+h[/tex]

Where the Vertex is:

[tex](h,k)[/tex]

In order to match each attribute to its corresponding equation, you need to find the Vertex, the Focus, and the Directrix of each parabola:

1. For the first parabola:

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

• You can identify that its Vertex is:

[tex](-4,-3)[/tex]

• By definition, the Focus of a horizontal parabola is:

[tex](h+\frac{1}{4a},k)[/tex]

In this case:

[tex]a=-2[/tex]

Then, you get that the Focus is:

[tex]=(-4+\frac{1}{4(-2)},-3)=(-4-\frac{1}{8},-3)=(-\frac{33}{8},-3)[/tex]

• By definition, the Directrix is:

[tex]undefined[/tex]

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