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Sagot :
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
[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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