Answer:
TRANSFORMING THE GIVEN INTO THE VERTEX FORM
Sa bahaging ito, ay gumagamit tayo ng Completing the Square Method upang makabuo tayo ng Vertex Form of Quadratic Function.
Solution
1. \purple{\boxed{y = x^2 - 2x - 3 }}
y=x
2
−2x−3
Factor out a.
\purple{\boxed{y = (x^2 - 2x) - 3 }}
y=(x
2
−2x)−3
\purple{\boxed{y = [(x^2 - 2x) +(\frac{-2}{2})^2] - 3 }}
y=[(x
2
−2x)+(
2
−2
)
2
]−3
\purple{\boxed{y = (x^2 - 2x + 1) - 3 }}
y=(x
2
−2x+1)−3
Factor out natin yung nasa loob ng parenthesis.
\purple{\boxed{y = (x - 1)^2 - 3 - 1 }}
y=(x−1)
2
−3−1
\purple{\boxed{y = (x - 1)^2 - 4}}
y=(x−1)
2
−4
Answer of Given (x² - 2x - 3)
\purple{\boxed{y = (x - 1)^2 - 4}}
y=(x−1)
2
−4
ang vertex form ng given na ito.
2. \purple{\boxed{y = -x^2 + 4x - 1 }}
y=−x
2
+4x−1
Factor out a.
\purple{\boxed{y = -[x^2 - 4x (\frac{-4}{2}^2)] - 1 - (\frac{-4}{2}^2)}}
y=−[x
2
−4x(
2
−4
2
)]−1−(
2
−4
2
)
Factor out yung nasa loob ng parenthesis at isimplify.
\purple{\boxed{y = -(x^2 - 4x + 4) - 1 - (-4)}}
y=−(x
2
−4x+4)−1−(−4)
\purple{\boxed{y = -(x - 2)^2 - 1 + 4}}
y=−(x−2)
2
−1+4
\purple{\boxed{y = -(x - 2)^2 + 3}}
y=−(x−2)
2
+3
yan lodi cakess
