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Graph the equation y=x²+8x+12 you must plot five points including the roots and the vertex

User Denian
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at the roots, y=0


\begin{gathered} \Rightarrow x^2+8x+12=0 \\ \Rightarrow(x+4)^2-(4)^2+12=0 \\ \Rightarrow(x+4)^2=4 \\ \Rightarrow x+4=\pm2 \\ \Rightarrow x=-4\pm2 \\ \Rightarrow x=-4+2\text{ or -4-2} \\ \Rightarrow x=-2\text{ or -6} \\ \end{gathered}

So two of the five points are:

(-2,0) and (-6,0)

At the vertex, dy/dx = 0


\begin{gathered} (dy)/(dx)=2x+8 \\ \text{When }(dy)/(dx)=0 \\ 2x+8=0 \\ \Rightarrow x=-4 \\ y=-4 \\ (-4,-4)\text{ is the vertex} \end{gathered}

When x=-1, y=5

(-1, 5)

When x=-3, y=-3

(-3,-3)

So the five points are

when x= -3, y=-3

User Tancho
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