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The quadratic 3x^2-24x+72+2x^2-6x+18 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?

 Jun 3, 2022
 #1
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a+b+c=47.

if we simplify and combine like terms, we will get 5x^2 - 30x + 90. 

it will then = 5(x^2 - 6x)+90

if we simplify the parenthesis, it will be 5[(x-3)^2 - 9] + 90. notice how I added the - 9 because -3 * -3 = 9.

Then, I'll multiply and distrubute the 5 to the -9, which is -45

If we combine like terms, the final will be 5(x-3)^2 + 45. 5-3+45=47.

 Jun 3, 2022

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