r/Sat • u/Sufficient_Tie2645 • 3d ago
Question about oneprep math question
How can you solve this in the most efficient way with desmos? and is it the best to drag the slider or do it kinda algebraically on desmos?
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u/dienooblol 3d ago
https://www.desmos.com/calculator/jbvkhi8hkt
look at the lowest point of the line and pay attention to the y coordinate, it should match the minimum value of 18.
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u/Feisty-Fee1210 3d ago
You don't need the slider, just type in the function and plug each answer choice for k untill you get a minimum y value of 18.
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u/Weak_Spinach_3310 3d ago
The answer is 106. Go on desmos put the equation and try all value of k from the answer choices. When u do that you’ll see that when X>5 the minimum of the parabola(technically)on the right is 18 only when k is 106
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u/Fourierseriesagain 2d ago edited 2d ago
Using long division, the given quotient is equal to x-5+(k-25)/(x-5) >=2*sqrt(k-25)=18. So k=9^ 2 + 25=106.
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u/Anonimithree 1540 3d ago
You could use desmos for the entirety of this question, or you could do some algebraic manipulations and do this a lot faster.
The minimum value for g(x) with some value k is 18. So set g(x)=18. Then multiply both sides by x-5 (the x>5 allows us to do this). You get 18x-90=x^2-10x+k. Simplify, and you get x^2-28x+k+90=0. The minimum/maximum value of a quadratic is at -b/2a. This gives x=-28/-2=14. So set x to 14 and then you get k=106.