How to Graph Vertex Form Quadratics

In this super short video, you'll learn how to graph a quadratic in vertex form with an a value greater than 1. We'll use a table, which is the easiest way to graph these functions! If you'd like the cheat sheet from the video, it's a free download on my blog here: www.scaffoldedmath.com/2020/0...
NEW VIDEO: Rather graph vertex form quadratics using patterns? • Graphing quadratics us...

[@aeriastic5369]

58 seconds of tutorial really thought me something than my teacher teaching 1 hr🤡

[@SpenserHoyt-fx6ku]

Sa Me

[@lisandrorios6400]

Omg i literally forgot how simple it was thx

[@scaffoldedmath]

Happy to help

[@justjadie-ov6do]

You have no idea how much time you just saved me. Thank you.

[@scaffoldedmath]

I'm so glad! Let me know if I can save you any more time with any other topics!

[@Be_artt]

THANK YOU SMMMMMMM!!!

[@scaffoldedmath]

My pleasure!

[@Vini_datguy]

Thanks so much!

[@Lavalamp-yk1zo]

Remember, the 4 if positive because it is inside the parenthesis. And also, if the function was (x+4)^2-8, then the four would be NEGATIVE

[@iFiidy]

Please elaborate.

[@Lavalamp-yk1zo]

@@iFiidy I am not sure if it is a rule, but when in vertex form, the number that is inside the parenthesis is either positive or negative. But remember, once you use this number to plot a point, it is now the opposite of what it was in the parenthesis. Example: In this video, the 4 is negative when inside the parenthesis. But once removed from the parenthesis, it becomes positive.

[@iFiidy]

@Lava lamp 2020 , ok. So is it safe to say that only when solving for vortex, this rule/ method applies?

[@Lavalamp-yk1zo]

@@iFiidy I would say so. So long as you are solving for the vertex, and the equation is in vertex form.

[@ezraora3498]

​@@Lavalamp-yk1zothat was my literal question man thanks love you

[@liamlambert2637]

Thankyou so much, this is very helpful

[@-mose191]

Dang I need a video of this that explains how to solve it! I know it's easy but, for me my teacher currently kinda suck at teaching it...

[@scaffoldedmath]

It's only easy if you know how to do it:) If you are solving, you set y (or f(x)) equal to 0 and solve for x. With the graph, you're looking for where the graph crosses the x axis. Those x values are the solutions.

[@surafeldeveloper]

You help second time thanks 🙏

[@scaffoldedmath]

[@maxminshew7409]

Thank you so much!

[@scaffoldedmath]

My pleasure!

[@sirtobis8583]

thanks homie

[@scaffoldedmath]

You bet

[@Chadowsky]

Dang, so this is how it's done. I'm probably not listening properly at school lol.

[@jeanchawa6372]

Help a lot

[@saulsalas2458]

Amazing!!! I learned so fast

[@klaus8910]

Simple method if you have graphing calculator; 1. Go to (y=) 2. Plug in the equation 3. Hit (Graph) 4. If you wanna take that risk, copy it. 5. [To access the table. Must still be on the graph.] Hit (2nd) & (Graph) 6. Copy it down, then find where the two Y intercepts sandwich. Example; |Y1, Y2| |1 , 4| |2 , 3| |3 , 4| In this example, the Vertex would be (2,3) Hope this helped

[@epsilon_music]

We don't in exams L

[@bluejacket4734]

THANKYOU! this will help me so much, now I dont have to write everything down 😂

[@user-ok6mz5rm3t]

I have watched a lot of tutorials n attended lectures but didn't understand then boom found this short video n learned something😂

[@scaffoldedmath]

I'm so glad to hear that :)

[@Torisashi123]

thanks❤

[@emuhu001]

Where do I get the paper you are writing on? I did not find it in your blog. Just the task activity and cheat sheet. Please help!! I need to teach this next week.

[@user-yz1of2do6n]

I’m trying to figure out how you get your for the table

[@AhuraRoohani]

How did this help? I am never understanding this

[@nebula6266]

So what is the axis of symmetry,max/min,max min value?

[@chrissystewart6268]

Let's learn I'm ready. I never learned this from school I feel a lot missing

[@noway7078]

I was wondering how come when using the distributive property, it gives the wrong answer?

[@adityagadhwal3099]

It will touch positive y axis at 24 and that is the full answer, else is correct 👍

[@kingjimmycraftofcalderonia2017]

Good simple method. Though, I like it better to just plot the vertex, convert the function to standard form, and then solve for x using the quadratic formula to find the x intercepts.

[@killilluminati321]

I can’t get the vertex in the function way why? What I’m I missing to solve it

[@killilluminati321]

What is the formula for the standard way

[@kingjimmycraftofcalderonia2017]

@@killilluminati321 Good question. The vertex of a quadratic is the highest or lowest point of a quadratic function (basically the middle of the curve of the function where the output changes from increasing to decreasing or decreasing to increasing. The easiest way to find the vertex of a quadratic formula is to have it on the vertex form of the function-which is generally f(x) = a(x+h)^2 +c. In this function, what the “a” do is tell you how wide or narrow the curve is, and whether the end points are going up or down. What “h” do is move the location of the function horizontally (opposite to its sign). What the “c” do is move the function vertically (corresponding to its sign). To find the x point of the vertex using the vertex form, all you need to do is set the grouped parentheses “x+h” equal to 0 and solve for x. In the example from the short: x-4 =0 x=4 To find the y point of the vertex using the vertex form, all you need to do is copy “c.” In the example of the video: y=c y=-8 Therefore, the vertex of the function y=2(x-4)^2 -8 is (4,-8)

[@kingjimmycraftofcalderonia2017]

@@killilluminati321 The standard formula for the quadratic equation is what follows: 0=ax^2 + bx + c. The only key detail to note is that “c,” like in a linear equation, is the y-intercept of the equation. To convert a quadratic function from vertex form to standard form, all you have to do is simplify the function with basic arithmetic. From the example of the video above: y = 2(x-4)^2 -8 Square the parenthesis: y = 2(x-4)(x-4) -8 Use FOIL to multiply the parentheses: y = 2(x^2 -8x + 16) - 8 Multiply 2 by the parenthesis: y = 2x^2 -16x +32 -8 Simplify like terms: y = 2x^2 -16x +24 Therefore, the standard form of this function is: f(x) = 2x^2 - 16x +24. From here, I know the y-intercept is 24, meaning the y-intercept is at (0, 24). Also, there are many ways to find the x-intercept of a quadratic function such as factoring, completing the square, and using the quadratic formula. Since I am generally lazy, I tend to use the quadratic formula method and use a calculator. The quadratic formula is: x=(-b (+|-) sqrt(b^2 -4ac))/(2a). All there is to be done is to substitute the variables from the standard form to the quadratic formula: Bonus tip: when you see a GCF (Greatest Common Factor) in the quadratic function, factor that GCF out to make the calculations less messy: y = 2x^2 - 16x + 24 Since they are all factors of 2, you get factor that 2 from the equation: 2(x^2 -8x + 12) Substitute the variables in the parenthesis to the formula: (8 (+|-) sqrt((-8)^2 -4(1)(12))/(2)(1). Using my trusty calculator: I can deter that x = 6, and x = 2. What this means is that the x-intercept of this function will be at (2,0) and (6,0).

[@jasonflores6302]

Can we pick any x from the x values?

[@scaffoldedmath]

You can! Because x is the independent variable there are infinite choices. I chose x values on either side of the vertex so they would be easy to graph. Zero is usually a nice x value to choose, too.

[@dr.pickle4980]

My teacher made this sound way harder than it is

[@theunluckycharm9637]

Im studying for my GED so I can go to HVAC trade school

[@KORR1116]

I love you

[@Rozzi123]

But why do you do the 4 x and -8 y and not use the 2 instead?😅

[@Stan4President]

Setting x to 0 would allow me to find the y intercept right?

[@scaffoldedmath]

Absolutely!

[@Ara_Rosy]

Which class question is it

[@ricardocastro3622]

Where do you get the numbers on X from

[@scaffoldedmath]

There are infinite choices for the x values when graphing a quadratic because the domain is (-infinity, infinity). But if you want to get that U shape, choose x values on either side of the vertex’s x value. After I identified the vertex from the equation (lmk if you need help with this), I chose a couple x values smaller than the vertex’s x value and a couple x values larger than the vertex’s x value. Then I just plugged those x values into the equation to find each y value.

[@irisRBLimited]

thx, got a test today and my dumb ass didn’t feel like revising any maths for the past 5 weeks (i missed the test and then never got a chance to do it and then the holiday happened and yeah) but to be fair idek what i really need to revise

[@scaffoldedmath]

Please don't give up. Your future self will thank you

[@ShadowBladez713]

f(x)=a(x-h)^2+k that is the formula. You would plug in the h and k so it would be f(x)=a(x-(-4))+(8) so thats the reason its a positive 4 because negative times negative is positive

[@02luvjae21]

why is it zero, instead of -4?

[@Datsu_Takahiro]

So are the vertexes just the middle and final number of the equation?

[@scaffoldedmath]

Pretty much. But the vertex's x value would be opposite the number inside the parenthesis. This is because you're looking for the value of x inside the parenthesis that would "zero" out the parenthesis. For example, (x + 18)^2 means the x value at the vertex is -18. (-18+18)^2 = 0

[@carultch]

The simple form of this kind of function is y=x^2. The vertex of the parent function occurs at the origin (0, 0). You then shift it horizontally by h, and vertically by k, in order to get the form of y=(x - h)^2 + k, and apply a scale factor of a in front of the parentheses to get the general form of y=a*(x-h)^2 + k. It is strategic to evaluate the vertex first when making your table of numbers to plot, because this tells you the symmetry of the function about a vertical line through the vertex. It also tells you where the curvature is greatest, and you'll need to plot in more detail to get the essence.

[@carultch]

If NOT given vertex form, but instead given expanded form y=a*x^2 + b*x + c, you can translate to vertex form as follows: Start with vertex form: y=a*(x - h)^2 + k Expand: y=a*(x^2 - 2*h*x + h^2) + k Distribute: y=a*x^2 - 2*a*h*x + a*h^2 + k This tells you that b = -2*a*h, and that c=a*h^2 + k. You can solve these for h and k as follows: h = -b/(2*a) k = c - b^2/(4*a)

[@ashishsharmavlogs246]

Beta maja a gya😂😂

[@anus7407]

Does it matter if the h (or x) is negative or not when you plug it in?

[@scaffoldedmath]

It'll just depend on the number and how it evaluates. You can rely on PEMDAS here. Say we had y = (x + 3)^2 - 8, we'd first find the vertex. The vertex here would be (-3, -8). Then we'd choose x values on either side of the vertex's x. This is the important part. We'd choose -2 for x and -4 for x because -2 < -3 < -4 and equally spaced to make things easier. To find a y, we'd plug in -2 for x and use PEMDAS: y = (-2 + 3)^2 - 8 ; y = (1)^2 - 8 ; y = -7 We have another point at (-2, -7) To find another y, we'd plug in -4 for x and use PEMDAS: y = (-4 + 3)^2 - 8 ; y = (-1)^2 - 8 ; y = -7 We have another point at (-4, -7) It's a good sign that the y values came out the same on either side of the vertex. This is because of the symmetry in quadratics. Hope this helps.

[@thantoo9119]

@@scaffoldedmath Thank you so so much .wish you happiness in your life.

[@scaffoldedmath]

@@thantoo9119 anytime you need help, I’m here😊

[@thantoo9119]

@@scaffoldedmath Thank you

[@thantoo9119]

@@scaffoldedmath You are such a humble person.

[@Not_black_imposter]

My brain malfunctioned trying to calculate this

[@scaffoldedmath]

Yikes! So sorry to hear that!

[@NAMANYT257]

woaa😉😉

[@scaffoldedmath]

You can find the cheat sheet from the video here as a free download: www.scaffoldedmath.com/2020/01/how-to-graph-vertex-form-quadratic-functions.html

[@rylesyl4910]

how did u get the -6? plss explain

[@scaffoldedmath]

(3 - 4)^2 is 1. Whenever you square a negative in ( ) it's positive. (-1)^2 = 1. Then multiply by 2 and subtract 8 to get -6.

[@shiaannee]

this is so simple, I'm just having a bit of trouble with the substitute part..😭

[@scaffoldedmath]

That can be the tricky part. 2(3 - 4)^2 = 2(-1)^2 = 2(-1)(-1) = 2

[@klaus8910]

@@scaffoldedmath explain simpler.

[@KHALEEL786QK]

Kya hai?

[@roniaaime2976]

Where did you get the negative 6 from?

[@shanadono]

That -6 comes from plugging 3 and 5 into the equation for x and evaluating.

[@scaffoldedmath]

(3 - 4)^2 is 1. Whenever you square a negative in ( ) it's positive. (-1)^2 = 1. Then multiply by 2 and subtract 8 to get -6.

[@draco8033]

how to get the number of y? how did you solve it i don't understand much

[@carultch]

You plug in the values you made up for x. To find the critical point of x, you look at the form of y=a*(x - h)^2 + k. The point (h, k) tells you the location of the vertex. Note that if there's a negative in front of h, it means h is positive, and positive in front of h, means h is negative. The h is the horizontal shift of the vertex. Then you evaluate the equation with values of x, immediately adjacent to x=h. You can also use the symmetry to your advantage, and save yourself time. Evaluate y at x=h+1, and you get y at x=h-1 for free. You know an equation in this form, has reflectional symmetry around x=h, since that's the nature of a parabola.

[@scaffoldedmath]

You can pick any x values you want. I chose x values on either side of the vertex x to keep things simple. Then you plug those x values into the equation to find their y values.

[@reliefmango6]

👍

[@Hehe-bh2zp]

How did you get 0?

[@scaffoldedmath]

if you want to find a zero (where y = 0), you can put 0 in for y and solve for x. In this case it would be 0 = 2(x - 4)^2 - 8. In the case in the video, we just happened to find the two zeros when we plugged in 2 and 6 for x.

[@one4me2foru38]

Wheres waldo?

[@siddhartha1348]

Why you join the points with free hand not using the scale❓

[@scaffoldedmath]

Scale?

[@siddhartha1348]

📏📏📏ruler

[@ronaldlorica5402]

paturo nmn mo Ng intercepts

[@alawiyyaaragasi804]

dko maclear?? Hehhe

[@pretzel6057]

Not tryna diss on teachers bro but like damn, it takes you 15 seconds, and days them multiple classes

[@hunain4769]

It was -4 why we wrote 4 there ?

[@shanadono]

The vertex's x coordinate is opposite the number inside the parenthesis. This is because it's the value of x that would cause the parenthesis to equal zero. (4 - 4)^2 = 0

[@cxllmegeo3557]

So did the 2 have anything to do with finding the vertex?

[@scaffoldedmath]

The 2 to the left of the parentheses does not affect the vertex at all. That 2 makes the sides of the parabola more steep, almost like slope does in a linear equation. The greater the number in that position, the steeper the sides of the parabola. You can also think of The parabola as getting skinnier as that number gets larger. But the vertex is always the same and is always based on the number inside the parentheses with X, and the number at the end of the equation.

[@cxllmegeo3557]

@@scaffoldedmath yea I just used the desmos graph calc just now I always forget the use of it lol

[@scaffoldedmath]

@@cxllmegeo3557 lol, I get it. Desmos is a great tool. I’m just a fossil and still enjoy graphing by hand.

[@Ash8a7]

@@scaffoldedmath wait i don't get it?? Why use the number 2??

[@shanadono]

@@Ash8a7 what do you mean?

[@tggleonardo.707]

Where 3 camefrom?

[@scaffoldedmath]

The 2, 3, 5 and 6 are all x values that you can choose. Once you know the vertex x value, choose 2 x values on either side of the vertex x value. You can choose any values, but keeping them close to the vertex x value makes the graph easier to plot.

[@mikhsly2]

vertex is h,k right?? what

[@carultch]

Yes. For any function f(x), to shift it horizontally by h to the right, you replace x with f(x - h). To shift it vertically by k, you add k external to this function. So to shift f(x) by h to the right, and k vertically upward, you get f(x - h)+k. Since the vertex of the original f(x) = x^2 function starts at the origin, that means the new vertex is at point (h, k).

[@cloutedchick5590]

When you were writing the equation, i was so confused and i am am😂

[@scaffoldedmath]

The equations I write in the video are the printed equation with the x values from the table plugged in.

[@BirdyKongy]

ayo i dont understand help

[@scaffoldedmath]

LMK what you don't understand. Sometimes it takes watching an example a few times to grasp what's going on. You can do it.

[@BirdyKongy]

@@scaffoldedmath ooo oki thanks for telling me

[@miteshraja4823]

Schools suck this literally taught you something complicated in 15 seconds. So what is it with schools then waste of time and money? Bad teaching structure? I wish it had this when I was school.

[@micah3080]

I don’t understand it at all

[@je6845]

You move too fast for me to understand what you're doing

[@Zhaolusi12345]

Blurred

[@Balls199]

I am still confused