# CAT 2014 | Question: 50

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A quadratic function $ƒ(x)$ attains a maximum of $3$ at $x = 1$. The value of the function at $x = 0$ is $1$. What is the value $ƒ(x)$ at $x = 10$?

1. $–119$
2. $–159$
3. $–110$
4. $–180$

b is correct ans.

process to solve; fisrst let the quadratic equation be ax^2 + bx + c

and x=0 as it is given from here we found c=1.

and by putting x=1 we find a+b=2

now final task as clu is given in question that max at x=1 is three so we all know maxima happens at x= – b^2 /4a

so putting it into initial equation we find relation b^2 = -8a so now using this into a+b=2 we found a quaratic like

(b-4)^2=0 so b=4 and a=-2 by putting all these values in first we found -2x^2+4x+1.

hence at x=10 value is -159.

note: if u dont know quadratic equation maximum better use derivative concept of finding maxima and minima.

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