For any quadratic expression f(x)=ax2+bx+c,a<0 and if (v,f(v)) is it's vertex, then y∈
A
[f(v),∞)
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B
[−f(v),f(v)]
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C
(−∞,f(v)]
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Solution
The correct option is C(−∞,f(v)] Given quadratic polynomial f(x)=ax2+bx+c,a<0 ⇒ The graph is an downward opening parabola as shown:
Here, we know for any quadratic expression with a<0, it's vertex will be the point of maximum.
Thus, it's range y∈(−∞,f(v)].