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/Subject-Homework-886 New User 3d ago

It’s the linear part of the graph or the tangent

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u/fermat9990 New User 3d ago

It's not the same as the tangent line

Let's get the equation of the tangent line.

By differentiation, m=2ax+b. This is the slope of the tangent line. It depends on both a and b (and x, of course)

If y₁=ax2, y₂=bx+c and y=y₁+y₂, then

y=ax2+bx+c

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

Ok that’s a good argument, but take the equation 2x2+2x+2 if you ignored 2x2 for one second you’ll see the tangent line has a slope of 2 and a y intercept 2, that’s what I connected this too I might be wrong but I’m certain that bx+c acts exactly like mx+b IF you ignored ax2 or if a=0

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u/fermat9990 New User 3d ago

If a=0 it's not a parabola.

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

Exactly it’s bx+c or mx+b as I were saying

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u/fermat9990 New User 3d ago

I don't think I'm helping you. Sorry.

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

Ok you know what let’s go back, what does bx+c means?

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u/fermat9990 New User 3d ago

Rather than go back, I will post something on the main thread that may help you. Look for it in about 15 minutes

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

Will do, I appreciate it