if f(x)=ax^2 +bx+c and f(x+3)=7x^2 +2x+5 find 1) a+b+c 2) a−b+c


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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

	$\underset{(i)}{\underset{⏟}{f (x) = {a x}^{2} + b x + c}} \land \underset{(i i)}{\underset{⏟}{f (x + 3) = 7 x^{2} + 2 x + 5}}$ $1) a + b + c 2) a - b + c$ $⇚≪ - . - . - . - ≫⇛$ $(i) : f (x) = {a x}^{2} + b x + c . . . . . . . . . . A$ $(i i) \Rightarrow f (x - 3 + 3) = 7 {(x - 3)}^{2} + 2 (x - 3) + 5$ $\Rightarrow f (x) = 7 x^{2} - 40 x + 62 . . . . . B$ $A & B \Rightarrow a = 7, b = - 40, c = 62$ $a + b + c = 7 - 40 + 62 = 29$ $a - b + c = 7 + 40 + 62 = 109$
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