If a quadratic is reflected on the y axis, why does b=0? If a quadratic in the form y=ax2+bx+c is reflected on the y axis, why then must b=0, making the equation in the form of y=ax2+c?

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If a quadratic is reflected on the y axis, why does b=0?  If a quadratic in the form y=ax2+bx+c is reflected on the y axis, why then must b=0, making the equation in the form of y=ax2+c?

Rosa Nicholson · Accepted Answer

Step 1  The maximum of the generic y=ax2+bx+c can be found via differentiation:  xvertex:2axvertex+b=0  If the shape is symmetric wrt the y axis, then the vertex must lie on the y axis itself, thus xvertex=0. This happens if and only if b=0.  Additionally, the intersections of the parabola with the x axis must be such that   x1=−x2⇒x1+x2=0,  with  x1, 2=b2a±b2−4ac2a⏞meh!  Thus,  x1+x2=ba  which is zero if and only if b=0.

Telering3b · Accepted Answer

I think what you mean to say is that the quadratic is symmetric about the y-axis. What that implies formally is that y(x)=y(−x). Try substituting the quadratic into that equation and see what happens.

If a quadratic is reflected on the y axis, why

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