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
