Respuesta :

reinhard10158

Step-by-step explanation:

y = x² - 4x + 7

the general vertex form is

y = m(x-h)² + k

to bring the part "x² -4x" to an expression of (ax + b)² we need to add 4, as "x² - 4x + 4" = (x - 2)².

and since we add 4 there, we need to subtract 4 overall again to keep the value of the expression the same :

y = x² - 4x + 4 + 7 - 4 = (x - 2)² + 7 - 4 = (x - 2)² + 3

and so, that is the vertex form :

y = (x - 2)² + 3

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's write the given equation into its vertex form ~

[tex]\qquad \sf  \dashrightarrow \: y = {x}^{2} - 4x + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = {x}^{2} - 4x + 4 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = {x}^{2} - 2x - 2x + 4 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = {x(}^{} x - 2) - 2(x - 2) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = (x - 2)(x - 2) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = (x - 2) {}^{2} + 3[/tex]

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