if-f-x-ax-2-bx-c-and-f-x-3-7x-2-2x-5-find-1-a-b-c-2-a-b-c-

Question Number 151081 by malwan last updated on 18/Aug/21

i f f (x) = {a x}^{2} + b x + c

a n d f (x + 3) = 7 x^{2} + 2 x + 5 f i n d

1) a + b + c 2) a - b + c

Answered by mr W last updated on 18/Aug/21

f (1) = a + b + c = f (- 2 + 3) = 7 {(- 2)}^{2} + 2 (- 2) + 5 = 29

f (- 1) = a - b + c = f (- 4 + 3) = 7 {(- 4)}^{2} + 2 (- 4) + 5 = 109

Commented by malwan last updated on 18/Aug/21

t h a n k y o u s i r

Commented by Rasheed.Sindhi last updated on 18/Aug/21

N i C e!

Answered by Rasheed.Sindhi last updated on 18/Aug/21

f (x) = {a x}^{2} + b x + c \land f (x + 3) = 7 x^{2} + 2 x + 5

1) a + b + c = ? 2) a - b + c = ?

- . - . - . - . - . - . - . -

a {(x + 3)}^{2} + b (x + 3) + c = 7 x^{2} + 2 x + 5

a (x^{2} + 6 x + 9) + b (x + 3) + c = 7 x^{2} + 2 x + 5

{a x}^{2} + (6 a + b) x + 9 a + 3 b + c = 7 x^{2} + 2 x + 5

a = 7 \land 6 a + b = 2 \land 9 a + 3 b + c = 5

a = 7 \Rightarrow b = - 40 \Rightarrow c = 5 - 63 + 120 = 62

a + b + c = 7 + (- 40) + 62 = 29

a - b + c = 7 - (- 40) + 62 = 109

Commented by malwan last updated on 18/Aug/21

t h a n k y o u s i r

Answered by Rasheed.Sindhi last updated on 18/Aug/21

\underset{(i)}{\underset{⏟}{f (x) = {a x}^{2} + b x + c}} \land \underset{(i i)}{\underset{⏟}{f (x + 3) = 7 x^{2} + 2 x + 5}}

1) a + b + c 2) a - b + c

⇚≪ - . - . - . - ≫⇛

(i) : f (x) = {a x}^{2} + b x + c \dots \dots \dots . A

(i i) \Rightarrow f (x - 3 + 3) = 7 {(x - 3)}^{2} + 2 (x - 3) + 5

\Rightarrow f (x) = 7 x^{2} - 40 x + 62 \dots . . B

A & B \Rightarrow a = 7, b = - 40, c = 62

a + b + c = 7 - 40 + 62 = 29

a - b + c = 7 + 40 + 62 = 109