Rewrite the function by completing the square f(x) =4x2+12x+9
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = 4x² + 12x + 9
The coefficient of the x² term must be 1 so factor out 4 from the first 2 terms
f(x) = 4(x² + 3x) + 9
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² + 3x
f(x) = 4(x² + 2()x +
-
) + 9
= 4(x + )² - 9 + 9
= 4(x + )²
Thus
f(x) = 4x² + 12x + 9 = 4(x + )²
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x ² - 4 = ( x - 2 ) ( x + 2 )
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )