How many critical points can a quadratic polynomial function have?

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Answer 1 · 2018-07-27T14:35:30

A quadratic polynomial function can have a single critical point.

A quadratic polynomial is a polynomial of second degree, in the form:

$f(x) = ax^2+bx+c$

with $a !=0$ .

By definition the critical points for $f(x)$ are the roots of the equation:

$(df)/dx = 0$

so:

$2ax+b = 0$

As this is a first degree equation, it has a single solution:

$barx = -b/(2a)$

so a quadratic polynomial function can have a single critical point, which by the way is the vertex of the parabola of equation:

$y = f(x)$