Question

dada a função f: R R definida por f9x) = ax² + b, com a, b ͼ R,

calcule a e b, sabendo que f(1) = 7 e f(2) = 22.

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Answer 1

Resposta:

Explicação passo-a-passo:

$f(1)=7\\\\a.1^{2}+b=7\\\\a+b=7\\\\\boxed{b=7-a}\\\\f(2)=22\\\\a.2^{2}+b=22\\\\4a+b=22\\\\4a+7-a=22\\\\3a=22-7\\\\3a=15\\\\\\a=\dfrac{15}{3}\\\\\boxed{a=5}\\\\b=7-a\\\\b=7-5\\\\\boxed{b=2}\\\\logo\\\\\boxed{f(x)=5x^{2}+2}\\\\Conferindo\\\\f(1)=5.1^{2}+2=5.1+2=5+2=7\\\\\\\\f(2)=5.2^{2}+2=5.4+2=20+2=22\\\\Confere.$