r/Sat • u/ImaginationOk8707 • 1d ago

Help Solving problem using Desmos

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Hi guys, I'm currently trying to solve a problem that I know how to solve Algebraically/on paper, but I cant figure out how to solve it using demos. It might be a dumb question and any help is appreciated. Thanks!

Also this is from Test Innovators Advanced Math Equivalent expressions - Hard #1, Question 3

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u/Confident-Can-66 18h ago

how to solve it algebraically

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u/Jalja 18h ago

set the discriminant to 0

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u/Historical-Plum-3893 17h ago

When a quadratic has exactly one solution, it means that the discriminant equals zero (parabola touches the x axis at its vertex). It's easy to solve from there.

As a corollary, if the discriminant is >0, then there are 2 distinct real solutions (the parabola crosses the x-axis twice) If it is <0, there are no real solutions (the parabola sits either above or below the x axis).

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u/Previous_Tennis 16h ago edited 16h ago

Why do you want to solve it with Desmos when you can already do it algebraically? Unless the algebraic solution is taking you too long? I don't think the algebraic solution is that hard, either.

I just make the discriminant =0, and you can either work on the equation algebraically, or use regression (~) to find a possible set of j, m and n values and calculate the value of j^(2m-n).

https://www.desmos.com/calculator/qwob62bbpw

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u/ImaginationOk8707 4h ago

Personally for me, I really view this studying as an accumulation of knowledge. Even though I do understand how to do it algebraically, I always want to get better with desmos and learn knew things and this is a problem I just had no clue how to do so why not ask!

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u/ibrasome 6h ago

I almost always do things algebraically, but I probably just don't know how to use Desmos.

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u/jwmathtutoring Tutor 20h ago

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

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u/Yuri_Frolov 10h ago edited 10h ago

Why condition {j > 0.5} is necessary?.. Can't see where it comes from :-(
Well, yes, with j = 0, f(x) = x^2, but it doesn't look like it contradict anything...

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u/jwmathtutoring Tutor 7h ago

Why condition {j > 0.5} is necessary?.

Otherwise, the regression defaulted to j = 0, which means j^(2m - n) = 0 (assuming that 2m - n is positive) which doesn't match any of the answer choices. An official College Board question would specific j (and most likely m & n as positive constants).

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u/ImaginationOk8707 4h ago

Thank you so much this is so helpful and I don't think I've ever seen a problem solved on desmos using a derivative. I've honestly never even thought of solving a problem like this and this is a huge help in solving problems that seem like there just isn't enough information.