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### Course: Algebra (all content)>Unit 7

Lesson 29: Comparing features of functions (Algebra 2 level)

# 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.

## Want to join the conversation?

• 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?
• 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.
• Are there any videos where we can do some exercises on getting the perfect square? I've seen it done on a few videos now but must have missed wherever that was.
• Am I watching the same video as the people in the comments? What do you mean when he completed the square?! WHAT SQUARE?! HUH?! Am I just dumb? I don't understand!
• can the lowest maximum value ever be the the x value of the vertex, or is it only for the y value of the vertex? I don't get why he doesn't use the x value of the vertex as part of his answer