How to Find the Vertex of a Parabola (NancyPi)

MIT grad explains how to find the vertex of a parabola. You can get the vertex from the parabola equation (standard form or vertex form). To skip ahead: 1) For how to find the X-COORDINATE of the vertex point from a STANDARD FORM equation of a parabola (like y = -2x^2 + 4x + 1), skip to time 0:16. 2) For how to find the Y-COORDINATE of the vertex, skip to time 1:34. 3) For how to get the vertex point from VERTEX FORM instead [like y = 2(x - 1)^2 + 3], skip to 2:24. 4) For what to do if the signs are confusing (ex. if the equation has X PLUS A NUMBER instead of x minus, like in y = 2(x + 3)^2 + 4), skip to 3:34. Nancy formerly of MathBFF explains the steps.

HOW TO FIND VERTEX:
How you find the vertex depends on whether the equation you're given is in "standard form" or "vertex form". How do you know if your problem is vertex or standard form? Each one has a very different form.

What is standard form? The STANDARD FORM equation is a quadratic polynomial and looks like y = ax^2 + bx + c without any parentheses (it has not been changed into another form by completing the square). If your equation looks like this, your vertex will be a point with an x-coordinate that is -b/(2a) where you can find a and b by comparing the standard form parabola formula to the equation you were given. Then, you can get the vertex y-coordinate by taking your original equation and plugging in the x-coordinate you found and simplifying until you've solved for y.

The VERTEX FORM is also a quadratic equation but is in the form y = a(x - h)^2 + k. It's easier and faster to find the vertex from the parabola vertex form, because the vertex is just the point (h,k) and h and k are values you can pull straight from the equation by matching the equation you were given with the vertex form formula that uses h and k. If your given quadratic equation has x plus a number, in parentheses, instead of minus a number, like y = 2(x + 3)^2, then you can rewrite the equation as subtraction of a number, like y = 2(x - (-3))^2, since adding 3 is the same as subtracting negative 3. This means that your h value will be negative 3.

Note: if you want to be able to convert your standard form into vertex form with a perfect square in your equation, you will need to "complete the square" first to get your parabola equation into vertex form.

On the graph of a quadratic function or parabola, the vertex is either the lowest point on the parabola (the minimum) if the parabola is opening up, or it is the highest point on the parabola (the maximum) if the parabola is opening down.

[novellaclaiborn]

math test tomorrow and you put it in a very simple understandable version, others seem to do too much and i get lost in there reasoning. straight to the point

[Pasperdu]

You helped me pass my first Calculus class! Glad to see you back in action! 💻🤓📖📚

[planomathandscience]

Forget her complete and easy way of explaining, she writes backwards, so nicely. My hero.

[angahlstrom]

That was SUPER helpful. She explained each steps (right when I thought she'd skip it like everyone else), and the rationale behind it all. Putting it into greater visual context would have helped me understand the more important "why" + "how this works on a graph" though. Thanks :)

[shmrnt]

Is she writing backwards? Because how can we see it perfectly but she is writing on the other side of glass?

[szejer]

You helped me pass trig and calc 1-2

Glad to see you back doing what your passionate about. And helping others

[melissacheckland]

Thanks so much! You have such a calming way of explaining what otherwise seem like complex math problems.

[lishalopez]

Thank you so much, my teacher has been explaining this for 2 days and no one understands it, including myself. I understood you in five minutes. Can’t wait to share this video with my friends!

[LuizMartins]

I spent hours trying to find a video that makes math easier than it looks and she does just that! She is amazing! I literally watched 20 seconds of this video and found what I needed!

[DSingh]

You helped me a lot in my Calculus classes. So happy I am done with all my math classes.

[Albertobelmonte]

The cool thing is -b/2a is derived from the quadratic formula. Also you can get the discrimanant from + or - square root b^2-4ac.

[PixuRz]

I’m done with math for college but just wanted to watch this vid cuz she makes math seem so easy lolol

[IvanMTG]

It's almost 12:30 AM in CA, but I don't care; Ima watch this!

[TheNaimi]

Thank you Nancy
You've made my life so much easier throughout the years <3

[LB_Tennessee]

Watched several videos (some within my online text) and I still didn't get it until I watched this video. Thanks, gal!

[vintagequill]

I was just thrown into 9th grade math whilst in 8th grade right in the middle of the year. This was so helpful, thank you thank you thank you!

[IICOR]

I received more useful information in the first 2 minutes of your video than the 300 videos I watch!!! Thank you!!!

[TJ-jxdx]

I really wish I found you at the beginning of the year... I'm actually shedding a tear over here.

[robertdiaz]

Your explanations and the handwritten notes are incredibly helpful. I do share Agasthya's question below, the one referencing the need for a negative in front of the 3 (in the value of h, as you explain at 04:15). Karlie and Napalm had discussed it a year ago and it seems a contrast to your explanation at 02:50, whereat you express the vertex as h-(-1), and that gives us the value of 1, but the 1 there was negative. I do see in Desmos that your answer is indeed (1, 3) but I'm left wondering if that could be the result of squaring 2 numbers). Could you please clarify that so that I may use your guidance in our tutoring session. Thanks so much.

[zacharyschoen]

Keep crushing it #NancyPi !!! I use your videos whenever I get stuck on my math problems in 1, 001 practice problems Algebra 2 for Dummies.