Exercícios - Definição

[size=150][center]Apresentamos anteriormente a definição da Função Quadrática, agora vamos trabalhar com alguns exercícios. [/center][/size]
Exercício 1
Exercício 2
[size=150][center]O que caracteriza duas funções quadráticas serem iguais são seus coeficientes. Sendo assim, considerando as funções [i][b]f(x)= ax²+ bx + c[/b][/i] e [i][b]g(x)= dx² + ex + j[/b][/i] , com [b]a [/b][math]\ne[/math][b] 0[/b] e [b]d [/b][math]\ne[/math][b] 0[/b], temos que: [br][br][math]\longrightarrow[/math] [b][i]f(x) = g(x)[/i][/b] [math]\Longleftrightarrow[/math] [b]a = d [/b][color=#cc0000](diferentes de zero)[/color], [b]b = e[/b] e [b]c = j[/b];[br][math]\longrightarrow[/math] [b]f(x) [/b][math]\ne[/math][b] g(x)[/b] [math]\Longleftrightarrow[/math] [b]a [/b][math]\ne[/math][b] d[/b] ou [b]b [/b][math]\ne[/math][b] e[/b] ou [b]c [/b][math]\ne[/math][b] j[/b].[br][br]Diante do exposto acima, determine quais das funções abaixo são iguais. [/center][/size]
Exercício 4
[justify][/justify][justify][/justify][size=150][justify]A área da região em forma de trapézio é dada por A = [math]\frac{\left(B+b\right)h}{2}[/math], em que a [i]B[/i] é a base maior, [i]b[/i] é a base menor e [i]h [/i]é a altura. Nesse trapézio, a área pode ser dada em função da base menor por uma lei do tipo [i]f(x) = ax² + bx + c[/i], com a [math]\ne[/math] 0.[/justify][center][img]data:image/png;base64,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[/img][br][br][/center]Com base nas informações apresentadas, determine: [br][br]a) A lei de formação dessa função.[br]b) Os coeficientes [i]a, b [/i]e[i] c[/i]. 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