what is the greatest possible value of the function f(x)?
(2) the straightline distance between the two roots of f(x) is 6.
THE OA IS NOT PROVIDED
We have to find the max possible value for the function. which is possible when x= 0 or x^2= 0
but we have found the value of x = 3 and -3 and corresponding value of k = 9
shouldn't we have found the value of K when x= 0 to show the max value of the function?
This is a different kind of sum which I am not able to fully comprehend? also here, is f(x) the equation of a parabola?
Can some one more clarify this for me.
Yes QLX ... Your approach is correct. In your approach also you are getting option C as correct which is indeed the right answer.
You are also correct when you say that it the equation of the parabola.
Parabola eq: f(x)=y=a(x^2) + bx + c
Comparing it with f(x)=k-x^2 :
We get 'b' is zero. And since 'a' is negative , we get a parabola that opens downward.
In a parabola equation, to get x-intercepts(i.e roots) , put y=0. And we get +/- sq. root of k ---> So the parabola cuts the x axis at two places.
The distance between these roots is mentioned as 6. So sq. root of k= 3.. Then k=9.
Now the point on y axis where x =0 will be the maximum value for the function. i.e. y=k .. Hence y=9 is maximum value.
This is the method to solve through parabola.
You just solved it in a different way, but yours is also correct