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TRANSFORMING THE GIVEN FUNCTION INTO VERTEX FORM
The vertex form of the quadratic function is:
\red{\boxed{y = a (x - h)² + k}}
y=a(x−h)²+k
Solution
Factor out a.
\red{\boxed{y = (x² - 4x) + 1}}
y=(x²−4x)+1
Complete the Perfect Square Trinomial (PST) by using Completing the Square.
\red{\boxed{y = [x² - 4x + (\frac{-4}{2})²] + 1 - (\frac{-4}{2})² }}
y=[x²−4x+(
2
−4
)²]+1−(
2
−4
)²
\red{\boxed{y = [x² - 4x + (-2)²] + 1 - (-2)²}}
y=[x²−4x+(−2)²]+1−(−2)²
Simplify.
\red{\boxed{y = (x² - 4x + 4) + 1 - 4}}
y=(x²−4x+4)+1−4
\red{\boxed{y = (x² - 4x + 4) - 3}}
y=(x²−4x+4)−3
Factor out the PST.
\purple{\boxed{y = (x - 2)² - 3}}
y=(x−2)²−3
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