Question
A quadratic function attains its minimum value of 5 at x=1 and holds a value of 6 at x=0. Find the value of the function at x=5
Answer: Option B
:
B
Standard form of a quadratic equation = f(x) = ax2+bx+c=0
Substitute x=0
Given that f(x)=c=6
Substitute x=1
a+b+c=5
a+b =-1................(1)
The minimum value of a function occurs at x=−(b2a), which is given as 1
Thus, 2a=-b
Substituting back in eqn (1) a=1 and b=-2
f(x)=x2−2x+6
Thus, at x=5, f(x)=21. Option (b)
Was this answer helpful ?
:
B
Standard form of a quadratic equation = f(x) = ax2+bx+c=0
Substitute x=0
Given that f(x)=c=6
Substitute x=1
a+b+c=5
a+b =-1................(1)
The minimum value of a function occurs at x=−(b2a), which is given as 1
Thus, 2a=-b
Substituting back in eqn (1) a=1 and b=-2
f(x)=x2−2x+6
Thus, at x=5, f(x)=21. Option (b)
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution