Exercícios - Pontos Importantes do Gráfico

Exercício 1
Exercício 2
Exercício 3
Exercício 4
O gráfico abaixo representa uma função quadrática do tipo [math]f\left(x\right)=ax^2+bx+c[/math], com [math]a\ne0[/math].[br][img]data:image/png;base64,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[/img][br][br]É possível afirmar que: [br]
Exercício Resolvido
Dada a função [math]f(x)=(m+2)x^2+(2m+1)x+m-1[/math], para quais valores de [math]m[/math] a função apresenta dois zeros?[br][br][i]Resolução: [/i]Sabemos que [math]f\left(x\right)[/math] possui duas raízes reais e diferentes quando [math]\Delta>0[/math]. A partir disso, vamos substituir os coeficientes da função [math]f[/math] na fórmula [math]\Delta=b^2-4ac[/math] e determinar para quais valores de [math]m[/math] delta é maior do que zero.[br][br]Temos que: [math]a=m+2[/math], [math]b=2m+1[/math] e [math]c=m-1[/math]. Substituindo, ficamos com: [br][br][math]\Delta=b^2-4ac=\left(2m+1\right)^2-4\left(m+2\right)\left(m-1\right)[/math] (i)[br][br]Note que: [math]\left(2m+1\right)^2=\left(2m+1\right)\left(2m+1\right)=4m^2+2m+2m+1=4m^2+4m+1[/math][br][math]4\left(m+2\right)\left(m-1\right)=4\left(m^2-m+2m-2\right)=4\left(m^2+m-2\right)=4m^2+4m-8[/math][br][br]Substituindo em (i), obtemos:[br][math]\Delta=4m^2+4m+1-(4m^2+4m-8)=4m^2+4m+1-4m^2-4m+8=+9[/math][br][br]Obtermos que [math]\Delta=9>0[/math], independente do valor de [math]m[/math]. Portanto, concluímos que para qualquer [math]m\in\mathbb{R}[/math] a função possui dois zeros.[br][br]
Exercício 5
Dada a função [math]f(x)=x^2+(3m+2)x+(m^2+m+2)[/math], para quais valores de [math]m[/math] a função tem um zero real duplo?
Exercício 6
Determine, em seu caderno, as coordenadas do vértice da parábola que representa a função quadrática [math]f(x)[/math] cujos zeros são -5 e -3 e o [i]coeficiente a[/i] é igual a 1.
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Information: Exercícios - Pontos Importantes do Gráfico