Question

Esboce o gráfico: Y= x²-6x+5

Answer 1

Segue esboço do gráfico em anexo.

$y=x^2-6x+5$


$\bullet\;\;$ Interseção com o eixo $y:$

Fazendo $x=0\,,$

$y=5$

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$\bullet\;\;$ Interseção com o eixo $x:$

Encontrando as raízes da equação:

$y=0\\\\ x^2-6x+5=0~~~\Rightarrow~~\left\{\! \begin{array}{l}a=1\\b=-6\\c=5 \end{array} \right.\\\\\\ \Delta=b^2-4ac\\\\ \Delta=(-6)^2-4\cdot 1\cdot 5\\\\ \Delta=36-20\\\\ \Delta=16$


$x=\dfrac{-(-6)\pm \sqrt{16}}{2\cdot 1}\\\\\\ x=\dfrac{6\pm 4}{2}\\\\\\ \begin{array}{rcl} x_1=\dfrac{6-4}{2}&~\text{ e }~&x_2=\dfrac{6+4}{2}\\\\\\ x_1=\dfrac{2}{2}&~\text{ e }~&x_2=\dfrac{10}{2}\\\\\\ x_1=1&~\text{ e }~&x_2=5 \end{array}$

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$\bullet\;\;$ Coordenadas do vértice:

$\bullet\;\;x_{_V}=-\,\dfrac{b}{2a}\\\\\\ x_{_V}=-\,\dfrac{(-6)}{2\cdot 1}\\\\\\ x_{_V}=\dfrac{6}{2}\\\\\\ \boxed{\begin{array}{c} x_{_V}=3 \end{array}}$

$\bullet\;\;y_{_V}=-\,\dfrac{\Delta}{4a}\\\\\\ y_{_V}=-\,\dfrac{16}{4\cdot 1}\\\\\\ y_{_V}=-\,\dfrac{16}{4}\\\\\\ \boxed{\begin{array}{c} y_{_V}=-4 \end{array}}$


Bons estudos! :-)

Answer 2

Resposta:

Explicação passo-a-passo:

Y=x-6x+