Find a and b

[nycmathguy]

Find a and b when the graph of
y = ax^2 + bx^3 is symmetric with respect to (a) the y-axis and (b) the origin. (There are many correct answers.)

Seeking steps to help me do this on my own.

 

[MathLover1]

Find a and b when the graph of
y = ax^2 + bx^3



The graph of a cubic function is symmetric with respect to its inflection point, and is invariant under a rotation of a half turn around the inflection point.

Even functions are symmetric with respect to the y-axis.
A function is "even" when: f(x) = f(-x) for all x


(a) the y-axis

the cubic curve is inversely symmetric about its point of inflection
cubic functions are inherently symmetric about the origin, also unless they have been translated


(b) the origin. (There are many correct answers.)

if a=0, b=1
or
if a=0, b=-1 or any other positive or negative real number

y = 0*x^2 + 1*x^3
y = x^3 =>is an dd functions have rotational symmetry about the origin

 

[nycmathguy]

Find a and b when the graph of
y = ax^2 + bx^3



The graph of a cubic function is symmetric with respect to its inflection point, and is invariant under a rotation of a half turn around the inflection point.

Even functions are symmetric with respect to the y-axis.
A function is "even" when: f(x) = f(-x) for all x


(a) the y-axis

the cubic curve is inversely symmetric about its point of inflection
cubic functions are inherently symmetric about the origin, also unless they have been translated


(b) the origin. (There are many correct answers.)

if a=0, b=1
or
if a=0, b=-1 or any other positive or negative real number

y = 0*x^2 + 1*x^3
y = x^3 =>is an dd functions have rotational symmetry about the origin

Ok. This question is more involved. I will read your reply at least twice.

 

[nycmathguy]

By the way, this is question 91 in Section 1.2.