Concavity [Solved!]

My question

In curve sketching with differentiation, the general curves section, there are no points of inflection written for the quadratic curve.
But from -1 to 1 it goes from negative to positive. Not clear as to why this would not be a point of inflection.

Relevant page

5. Curve Sketching using Differentiation

What I've done so far

My work includes reading and re-reading and re-reading the section Finding points of inflection, and also reviewing the examples given.

X

In curve sketching with differentiation, the general curves section, there are no points of inflection written for the quadratic curve.
But from -1 to 1 it goes from negative to positive.  Not clear as to why this would not be a point of inflection.
Relevant page

<a href="https://www.intmath.com/applications-differentiation/5-curve-sketching-differentiation.php">5. Curve Sketching using Differentiation</a>

What I've done so far

My work includes reading and re-reading and re-reading the section Finding points of inflection, and also reviewing the examples given.

Continues below

Re: Concavity

@Phinah: Please have another look at the definition of a point of inflection.

It's where the concavity of the curve changes sign. That is, where it changes from a "U shaped" curve to an "n shaped" curve (or vice versa).

However, a quadratic curve (a parabola) is "U shaped" everywhere (or "n shaped" if the number in front of the x^2 term is negative).

U-shaped (e.g. y=x^2+2x+5)

n-shaped (e.g. y=-x^2-3x+7)

So it won't have a point of inflection.

X

@Phinah: Please have another look at the definition of a point of inflection.

It's where the <b>concavity</b> of the curve changes sign. That is, where it changes from a "U shaped" curve to an "n shaped" curve (or vice versa).

However, a quadratic curve (a parabola) is "U shaped" everywhere (or "n shaped" if the number in front of the x^2 term is negative).

<b>U-shaped</b> (e.g. y=x^2+2x+5)

[graph]310,250;-4.5,3.5;-0.5,10.3,1,2;x^2+2x+5,[/graph]

<b>n-shaped</b> (e.g. y=-x^2-3x+7)

[graph]310,250;-4.5,3.5;-0.5,10.3,1,2;-x^2-3x+7,[/graph]

So it won't have a point of inflection.

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