Respuesta :

burgarabesque
To solve this, use the ‘completing the square’ strategy.
Leave a space to make the first two values a perfect square.
y=(x^2-2x___)-3
Divide -2 by 2 and square that number to put in the blank. Then subtract that number from outside.
y=(x^2-2x+1)-3-1
Simplify!
y=(x-1)^2-4
It is in vertex form now ;)

Please make my brainliest ,’-)
luisejr77

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

Step-by-step explanation:

The vertex form of the equation of a parabola is:

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

Where (h,k) is the vertex.

To obtain this form, we need to complete the square:

Move the 3 to the other side of the equation:

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

Add this value to both sides of the equation: [tex](\frac{-2}{2})^2=1[/tex]

[tex]y+3+1=x^2-2x+1[/tex]

[tex]y+4=x^2-2x+1[/tex]

Then, rewriting:

 [tex]y+4=(x-1)^2[/tex]

Finally, we must solve for "y", getting the equation of the parabola in vertex form:

 [tex]y=(x-1)^2-4[/tex]

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