14 - Graphing Quadratic Functions - Max & Min Values - Part 1

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Twitter: / jasongibsonmath
In this lesson, we will learn how to find the maximum and minimum values of any given parabola. This is used to find the vertex of the parabola and sketch the graph of the parabola.
The max value only occurs if the parabola opens down. The min value only occurs if the parabola opens up. We discuss how to find if the parabola has a max or min value and how to calculate the value.

[@Ilona632]

Was just going over stuff I learned in school long time ago. And saw this video. 👍Very well explained.

[@Alibern7]

3:52 helped me I was trying to figure out if it’s still a max or min when the quadratic function was facing up or down

[@PatrickCraig-lh5is]

Could you also state that (x + b/2a)^2 is the same as (x - (-b/2a))^2 and read the shift _h_ directly as -b/2a? Since the vertex form is always y - k = (x - h)^2, you would need to think of an addition on the right in terms of a subtraction: subtracting a negative is the same as adding a positive, and this would make the leftward shift obvious (no memorization of "do the opposite of the sign" needed). In the case of a subtraction being given in the first place, it could be seen as subtracting a positive (meaning rightward shift). (x - (+b/2a))^2 I know that students are often taught to think of subtraction in terms of addition in pre-algebra, so asking them to go the other way could potentially be confusing. Just curious as to what others think of this.

[@bhavyanayak4342]

Wonderful explanation sir, this helped a lot. Thank you!

[@rob7633]

Thanks your a great teacher learned alot.

[@EdwinChibesa]

This is great work

[@evanceogada2054]

great work indeed

[@chadetrikrout]

Excellent explanation Sir...

[@netuno60]

Great explanation sir!

[@princelolowu7726]

Watching this in 2022 and this was so helpful

[@aaminadurrani5131]

well explained...

[@amberbazanx3]

Thank you!!!

[@fanuelmuntanga355]

Great 🎉thanks

[@bidarvandi]

2 unit shifted over is x and y one unit is up are vertex could not get it

[@hemarajue2736]

It also works while factoring 'a' i.e ax^2+a/abx=a(x^2+b/ax).

[@Panamaxro2012]

thats scary

[@hemarajue2736]

@@Panamaxro2012 nothing to scare,it is just a basic rule. Here we need to factor out 'a' but there is no factor 'a' in the second term. So I multiplied a/a with the second term.

[@abnerpratt2619]

How did you find the (f)?

[@racquelsabesaje4562]

x=-b/2a=- 8/2(2)= - 8/4= -2

[@racquelsabesaje4562]

y=2(4)-16

[@racquelsabesaje4562]

y=8-16

[@racquelsabesaje4562]

f(x)=2x2+8x

[@racquelsabesaje4562]

y(f-2)=2x2+8x

[@racquelsabesaje4562]

vertex -2 -8

[@racquelsabesaje4562]

y=f(-2)=2(-2)2+8(-2)

[@jeremycornish-ford2435]

Do you still love peanut butter and jelly?

[@racquelsabesaje4562]

y=f(-b/2a)

[@racquelsabesaje4562]

y= - 8

[@racquelsabesaje4562]

x=(-b/2a)

[@racquelsabesaje4562]

a=2 b=8

[@racquelsabesaje4562]

x= -2

[@racquelsabesaje4562]

formula

[@patricklux9870]

math is the most stupid thing ever like learning system of someone who just imagined some numbers and things

[@MathAndScience]

Actually nothing could be further from that truth. Math is directly responsible for physics, chemistry and all branches of engineering. So without math, you wouldn’t have any electronic devices, no phones, no internet, no medicine, no surgery, no power generation. So without math, you should build a hut and start hunting for food in the dark. Good luck!

[@dharshinia9378]

@@MathAndScience without maths, he can't even build a hut🤣lol

[@sarthak8350]

Math is stupid says a guy who uses smartphone

[@WilliamCooper2005]

unanimous condemnation of your bad opinion.