Quadratic Graph

Algebra Level 2

The maximum point of the function f ( x ) f(x) = a x 2 ax^{2} + a x + 14 x ax+14x + a − 16 a-16 is on the x-axis and the y-intercept is ( m , n ) (m,n) . If so, what is m + n m+n ?


The answer is -18.

Jovan Alfian Djaja by Jovan Alfian Djaja , 18, Indonesia

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1 solution

It is said that the maximum point of the function is on the x-axis . That means the discriminant of the function is 0.

By using the discriminant equation and simplifying, we have 2 options for the value of a a , -2 and 98 3 \frac{98}{3} . Since the question asks for maximum, we choose -2.

By substituting a a = -2 and evaluating f ( 0 ) f(0) , we have (m,n) = (0,-18) and m+n =-18

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Good problem. But you used the variable a a for two different things. I recommend you change it.

James Wilson - 5 months ago

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I just realized it. Thank you for noticing me.

Jovan Alfian Djaja - 5 months ago

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No problem :)

James Wilson - 5 months ago

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