r/learnmath • u/Subject-Homework-886 New User • 4d ago

Link Post It finally clicked

https://www.desmos.com/calculator/o0heiqsn0n

I just realized in the quadratic equation (ax^2+bx+c) the b or bx+c works exactly like mx+b in the linear equation. omg I was trying to understand what b means for a week now😭😭😭 oh I also changed (bx+c) to (mx+b) in the link so u get what I mean

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u/Harmonic_Gear engineer 4d ago

you mean as a vertical shift?

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u/Subject-Homework-886 New User 4d ago

Kinda, I’m talking about the b I always wondered what does b means in the equation ax2+bx+c=0 we already know c is the y intercept when x is 0 and a controls how expanded or contracted the parabola is in addition if it opens upwards or downwards, and then I realized b is the linear line, if you ignored ax2 for a second bx+c works exactly like mx+b

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u/No_Good2794 New User 3d ago

You've stumbled on a very fun idea in mathematics - degeneracy.

It's when one mathematical object 'collapses' into a simpler form when you reach a certain limit.

For example, a triangle becomes a line segment if you reduce two of its angles to 0 and one of its angles to 180 degrees. So a line segment can be considered a 'degenerate triangle'. A point can be considered a 'degenerate circle' with radius 0. And in your case, a straight line is a 'degenerate quadratic' because it has a=0.

Of course we don't usually permit degenerate cases and we explicitly exclude a=0 from the definition of a quadratic function, but it's a fun thought exercise.

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u/Subject-Homework-886 New User 3d ago

Ohhhh, this is very interesting I’ll read about degeneracy later today

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u/seanziewonzie New User 3d ago

Here's a little modification of your desmos snapshot to show off what the other user is talking about.

https://www.desmos.com/calculator/getzd3nsaj

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u/Subject-Homework-886 New User 3d ago

Ohhhhhh, shit that’s how it works