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The quadratic -6x^2+36x+216 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?

Jun 26, 2018

#1
+22343
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The quadratic -6x^2+36x+216 can be written in the form a(x+b)^2+c,

where a, b, and c are constants.

What is a+b+c?

$$\begin{array}{|rcll|} \hline && -6x^2+36x+216 \\ &=& -6(x^2-6x) + 216 \\ &=& -6[ (x-3)^2 -9 ] +216 \\ &=& -6(x-3)^2 + 6\cdot 9 + 216 \\ &=& -6(x-3)^2 +54 + 216 \\ &=& -6(x-3)^2 + 270 \quad & | \quad \text{compare with a(x+b)^2+c} \\\\ a &=& -6 \\ b &=& -3 \\ c &=& 270 \\ a+b+c &=& -6-3+270 \\ \mathbf{a+b+c} & \mathbf{=}&\mathbf{ 261 } \\ \hline \end{array}$$

Jun 26, 2018

#1
+22343
+1

The quadratic -6x^2+36x+216 can be written in the form a(x+b)^2+c,

where a, b, and c are constants.

What is a+b+c?

$$\begin{array}{|rcll|} \hline && -6x^2+36x+216 \\ &=& -6(x^2-6x) + 216 \\ &=& -6[ (x-3)^2 -9 ] +216 \\ &=& -6(x-3)^2 + 6\cdot 9 + 216 \\ &=& -6(x-3)^2 +54 + 216 \\ &=& -6(x-3)^2 + 270 \quad & | \quad \text{compare with a(x+b)^2+c} \\\\ a &=& -6 \\ b &=& -3 \\ c &=& 270 \\ a+b+c &=& -6-3+270 \\ \mathbf{a+b+c} & \mathbf{=}&\mathbf{ 261 } \\ \hline \end{array}$$

heureka Jun 26, 2018