Let $f(x) = a^2x^2 + 2bx + c$ where, $a \neq 0$, $b, c$ are real numbers and $x$ is a real variable then

Question and options

Let

f(x) = a^2x^2 + 2bx + c

where,

a \neq 0

b, c

are real numbers and

x

is a real variable then

Correct answer: B - $f(x)$ has a minimum and no maximum

The leading coefficient a^2 > 0, so the parabola opens upward: it has a minimum at the vertex and grows without bound, so there is no maximum.