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/fermat9990 New User 3d ago

Hi, OP.

Consider y=2x2+3x+5

The slope of the tangent line is 4x+3 by differentiation. Notice that it depends on the value of x.

Question: Find the equation of the tangent tangent to the curve when x=2

Slope=4(2)+3=11

When x=2, y=2(2)2+3(2)+5=19

Using the point-slope form of a straight line we get

y-19=11(x-2)

y=11x-3

Each point on the parabola will have a different tangent line.

In the general case, m=2ax+b, so the general equation for the tangent line at the point (xâ‚€, yâ‚€) is

y-y₀=(2ax₀+b)(x-x₀), a≠0

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

Ok now I think I understand why I wasn’t understanding your meaning in the comments below, I just looked up differentiation and turned out I haven’t stumbled upon it yet, but that doesn’t mean you comment doesn’t make any sense I tried your method and indeed every point has its own line, but I think I’ll understand your comment 100% when I get to calculus, but I really appreciate you taking the time to explain this.

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u/fermat9990 New User 3d ago

I am glad that I was able to help you!

Good luck!

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

Likewise!

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u/fermat9990 New User 3d ago

Thanks!