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# quadratic

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The quadratic -6x^2+72x+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 27, 2022

### Best Answer

#1
+2448
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Note that $$(x+b)^2 = x^2 + b^2 + 2xb$$

This means that $$a = -6$$

Also, note that $$-6 \times 2xb = 72x$$, because it is the only term with x.

This means $$b = -6$$

Expanding what we have gives us: $$-6x^2 + 72x -216$$, so we add 432, to make the constant positive.

This means $$a + b + c = \color{brown}\boxed{420}$$

Jun 27, 2022

### 1+0 Answers

#1
+2448
0
Best Answer

Note that $$(x+b)^2 = x^2 + b^2 + 2xb$$

This means that $$a = -6$$

Also, note that $$-6 \times 2xb = 72x$$, because it is the only term with x.

This means $$b = -6$$

Expanding what we have gives us: $$-6x^2 + 72x -216$$, so we add 432, to make the constant positive.

This means $$a + b + c = \color{brown}\boxed{420}$$

BuilderBoi Jun 27, 2022