Maximum of Minimum

Algebra Level 2

Let m m be the minimum value of the quadratic function f ( x ) = x 2 + 2 a x + 18 a + 5. f(x)=x^2+2ax+18a+5. What is the sum of the maximum possible value of m m and the value of a a maximizing m ? m?

95 85 80 90

View wiki
Mahindra Jain by Mahindra Jain

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Pulkit Gupta
Dec 1, 2015

Lets apply completing the square method to find the minimum value, m , of this quadratic.

The given quadratic may be written as ( x + a ) 2 x+a)^{2} + 18a + 5 - a 2 a^{2}

Clearly, m = 18a + 5 - a 2 a^{2}

Now we again employ completing the square method to obtain maximum value of m.

Clearly, m = 5 + 81 - ( a 2 a^{2} - 18a + 81 - 81) = 86 - ( a − 9 ) 2 (a-9)^{2}

Therefore, maximum value of m = 86 is obtained at a = 9 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...