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# Comparing maximum points of quadratic functions

Given several quadratic functions represented in different forms, Sal finds the one with the lowest maximum value. Created by Sal Khan.

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• i have literally no clue whatsoever what that last bit where he "completed the square" was. can anyone help me with this?
• Completing the square is a mathematical concept which was created to find the X intercepts of a function (as seen at ). It does the exact same thing as the quadratic formula, but is often easier to do, when the coefficients and whole numbers and you don't have a calculator. It's really impossible to explain how to do this in one comment, but take a look at this website that gives examples and shows the process of completing the square. http://www.purplemath.com/modules/sqrquad.htm
• Sal lost me in the last 30 seconds of the video. The negative: - (x - 3) seemed to disappear with no explanation. What happened, To me it seems that x-3 = 0 would produce x = 3, but the preceding negative would make x = -3 and y = 8. Is that what happened? Some of these videos assume that we can follow ideas with leaps of imagination that my current math knowledge will not permit. I need to see EACH STEP EXPLICITLY EXPLAINED!
• Haha, I'm answering this 7 years later...
Anyway, x = 3 because in order to find the y-value, -(x-3)^2 has to equal 0. And the only way that's possible is if x = 3. If you plug in x = 3, then -(3-3)^2 = 0. I guess that equals -0, but -0 and 0 are the same thing. If x = -3 like you thought, then -(-3-3)^2 = -36, and that doesn't help to find the y-value.
Hope this helped!
• For the minimum/maximum, is the vertex the same thing?
• Or to put it another way, for a given parabola, the parabola's maximum or minimum value will occur at its vertex.
• Where did the 6x go when he converted it to a perfect square?
(1 vote)
• He factored the quadratic. (x^2 - 6x + 9) = (x - 3)(x - 3) = (x - 3)^2.
• I solved this problem without completing the square. I just tried out x=2 in f(x)
f(2) =-4 +12 -1 =7
If a point of f(x) is 7 then its maximum cannot be less than -1 so of the three functions the one with the lowest maximum is h
• Well... that's a valid way to do it in this particular case, but consider the fact that you sort of got lucky there. If `f(x)` had been shifted down (and contained the lowest maximum), you wouldn't be able to used that method.
• Why did Sal use -1 as the maximum value? (at ) There is also 4 (x-coordinate). Can't he just take the average of the two? But if he does, it becomes a crazy fraction. Can somebody please clear this up for me? Thank you so much.
• He's looking for max. g(x) coordinate not the x coordinate
• At the beginning of the video we're given a quadratic function g(x) for which only a table of x & y values are provided. My question is how do we find the quadratic equation of such a function for which only a few x & y values are given.
• Hello Avishek, in this problem we only need the max value, not the equation. There is an interesting property of quadratics in that, every quadratic equation,when graphed, has either a maximum or a minimum. What do i mean by this? well with the -x^2+6x-1 for example, the max is 8, and no matter what x-value we choose, we will never find a higher value. Hence, since the table for g(x) shows that g(0) =5 and the values of both adjacent x-values are less, we can conclude that 5 is the maximum value for g(x). As for finding the equation for g(x)? It could be approximated accurately, but it would take a good bit of guess work, or calculus. Hope this helps! Side Note: after some calculations, g(x) appears to be -(x^2)+5 though this is just what i came up with.
(1 vote)
• At Sal begins using completing the square method in order to find the lowest maximum value.
Can I use X= -b/2a where X gives the lowest maximum value and b and a are the coefficients of x and x^2 respectively.
Thanks.
PS I did get the correct answer using this method. He showed it in finding the x coordinate of finding the vertex of a parabola.
(1 vote)
• By completing the square, Sal finds a quadratic (x - something)^2 that is shifted up or down by some other thing. X=-b/2a does not take into consideration the "c" term or constant. The quadratic shows explicitly the min or max value of this function.