Completing the Square

Algebra Level 2

If the coordinate of the minimum point on the curve:

y = x 2 + 13 x 5 + 669 20 y=\frac{x^2 + 13x}{5} + \frac{669}{20}

is ( a , b ) (a,b) , find a + b a+b


The answer is 18.5.

Luca Seemungal by Luca Seemungal , 21, United Kingdom

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1 solution

Kay Xspre
Nov 22, 2015

We rearrange the equation into y = 4 ( x 2 + 13 x ) + 669 20 y = \frac{4(x^2+13x)+669}{20} , which equals to y = 4 ( x 2 + 13 x + 42.25 ) + 500 20 = 1 5 ( x + 6.5 ) 2 + 25 y = \frac{4(x^2+13x+42.25)+500}{20} = \frac{1}{5}(x+6.5)^2+25 Hence, the minimum point is ( − 6.5 , 25 ) (-6.5, 25) and a + b = 18.5 a+b = 18.5

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