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The standard form of the equation of a parabola is x = y2 - 4y + 20.
What is the vertex form of the equation?

A. x = (y - 4)2 + 4
B. x = (y - 2)2 + 16
C. x = (y - 2)2 + 4
D. x = (y - 4)2 + 12

Respuesta :

Neuron
If you would like to find the vertex form of the equation, you can calculate this using the following steps:

x = y^2 - 4 * y + 20
x = (y - 2)^2 - 4 + 20
x = (y - 2)^2 + 16

The correct result would be B. x = (y - 2)^2 + 16.

Answer:

The correct option is B.

Step-by-step explanation:

The given equation is

[tex]x=y^2-4y+20[/tex]

It can be written as

[tex]x=(y^2-4y)+20[/tex]

Add and subtract [tex](-\frac{b}{2a})^2[/tex] in the parenthesis.

[tex](-\frac{b}{2a})^2=(\frac{-4}{2(1)})^2=(-2)^2=4[/tex]

Add and subtract 4 in the parentheses.

[tex]x=(y^2-4y+4-4)+20[/tex]

[tex]x=(y^2-4y+4)-4+20[/tex]

[tex]x=(y+2)^2+16[/tex]

Therefore option B is correct.

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