square the binomial and compare the results to find k
(2x-3)^2 = 4x^2 - 12x + 9
(2x-3)^2 + k = 4x^2 - 12x + 13
check your calculations
The equation f (x) = 4x^2 - 12x + 13 is written as the equivalent function f (x) (2x-3)^2 + k. What is the vale of k?
I got an answer from someone else, and I'm not quote sure if I understood their answer clearly, but I got 9? Is it correct? This is very important because I have to finish this benchmark, and then I have to finish another and I only have a few hours left to do it! I really need help!
4 answers
4 x² - 12 x + 13 = ( 2 x - 3 )² + k
______________________________
Remark:
( m - n )² = m² - 2 ∙ m ∙ n + n²
( 2 x - 3 )² = ( 2 x )² - 2 ∙ 2 x ∙ 3 + 3² + k
_______________________________
4 x² - 12 x + 13 = ( 2 x )² - 2 ∙ 2 x ∙ 3 + 3² + k
4 x² - 12 x + 13 = 4 x² - 12 x + 9 + k
Subtract 4 x² - 12 x + 9 to both sides
4 x² - 12 x + 13 - ( 4 x² - 12 x + 9 ) = ( 4 x² - 12 x + 9 ) + k - ( 4 x² - 12 x + 9 )
4 x² - 12 x + 13 - 4 x² + 12 x - 9 = k
4 x² - 4 x² - 12 x + 12 x + 13 - 9 = k
4 = k
k = 4
4 x² - 12 x + 13 = ( 2 x - 3 )² + 4
______________________________
Remark:
( m - n )² = m² - 2 ∙ m ∙ n + n²
( 2 x - 3 )² = ( 2 x )² - 2 ∙ 2 x ∙ 3 + 3² + k
_______________________________
4 x² - 12 x + 13 = ( 2 x )² - 2 ∙ 2 x ∙ 3 + 3² + k
4 x² - 12 x + 13 = 4 x² - 12 x + 9 + k
Subtract 4 x² - 12 x + 9 to both sides
4 x² - 12 x + 13 - ( 4 x² - 12 x + 9 ) = ( 4 x² - 12 x + 9 ) + k - ( 4 x² - 12 x + 9 )
4 x² - 12 x + 13 - 4 x² + 12 x - 9 = k
4 x² - 4 x² - 12 x + 12 x + 13 - 9 = k
4 = k
k = 4
4 x² - 12 x + 13 = ( 2 x - 3 )² + 4
Thank you!
F(x) = 4x^2 - 12x + 13.
h = -B/2A = 12/8 = 3/2.
K = 4(3/2)^2 - 12(3/2) + 13 = 9 - 18 + 13 = 4.
Vertex Form: F(x) = a(x-h)^2 + k. = 4(x - 3/2)^2 + 4.
h = -B/2A = 12/8 = 3/2.
K = 4(3/2)^2 - 12(3/2) + 13 = 9 - 18 + 13 = 4.
Vertex Form: F(x) = a(x-h)^2 + k. = 4(x - 3/2)^2 + 4.
0 answers