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Help needed with the coordinates of points of intersection!

0
196
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Mar 19, 2018

#1
+22152
+1

Help needed with the coordinates of points of intersection!

a:

$$\begin{array}{|rcll|} \hline y &=& x^2-6x \\ y &=& -8 \\\\ x^2-6x &=& -8 \\ x^2-6x+8 &=& 0 \\ x &=& \dfrac{6\pm \sqrt{36-4\cdot 8}}{2} \\ x &=& \dfrac{6\pm \sqrt{4}}{2} \\ x &=& \dfrac{6\pm 2}{2} \\ x &=& 3\pm 1 \\ \\ x_1 &=& 4 \qquad y_1 = -8 \\ x_2 &=& 2 \qquad y_2 = -8 \\ \hline \end{array}$$

b:

$$\begin{array}{|rcll|} \hline y&=& x^2-24 \\ y &=& -2x \\\\ x^2-24 &=& -2x \\ x^2+2x-24 &=& 0 \\ x &=& \dfrac{-2\pm \sqrt{4-4\cdot (-24)}}{2} \\ x &=& \dfrac{-2\pm \sqrt{100}}{2} \\ x &=& \dfrac{-2\pm 10}{2} \\ x &=& -1\pm 5 \\\\ x_1 &=& 4 \qquad y_1 = -2\cdot 4 = -8 \\ x_2 &=& -6 \qquad y_2 = -2\cdot (-6) = 12 \\ \hline \end{array}$$

Mar 19, 2018