Three Forms of Quadratic Equations

We will quickly review three forms of the equation of a parabola. These are the standard form (which quickly tells you the y-intercept), the vertex form (which gives you the vertex [h,k] ), and the factored form, which tells you the roots, or zeros, of parabolic functions. We'll do a worked example to convert between the three forms of parabolic equations. We'll complete the square to find the vertex form, and find features of the graph of a parabola, including its axis of symmetry, vertex, y-intercept, minimum value, domain, range, and complex roots.

[@ibrahimsuhail6435]

Yes this deepen my understanding on quadratics.. Thanks!!

[@kagm2730]

thank you so much this helped me a bunch to understand quadratics!!!!

[@dr.piercesphysicsmath9071]

Terrific! 👍

[@raptor_xvii9464]

Helped alot! also the determination of solutions can be done through discriminant, b^2-4ac

[@zeno_y]

This is very helpful for connecting those three forms of quadratics. Thank you.

[@dr.piercesphysicsmath9071]

Thank you for taking the time to give feedback. I appreciate it.

[@HowardPilyo]

I really like the explanation ❤

[@jennawright7136]

Seems like a good video except I would not recommend this for beginners at all because I thought this was supposed to an introduction and I did not understand anything that was said in the video. I think explaining it in a simple way from the basics would be more helpful for people who have never done the three different forms before.

[@dr.piercesphysicsmath9071]

Thanks for the feedback! We try to help everyone, but when we miss the mark, the feedback makes us better. 👍

[@jojotag5344]

I wasn't understanding anything until you showed us (-b/2a), then everything made sense XD thank you!

[@dr.piercesphysicsmath9071]

Excellent. 👍

[@Olivia-nn6zb]

urgent question; how come we ended up with both positive 3 and 4 for (3,4)? shouldn't one of them end up negative, because we're adding AND subtracting 3squared? how come they were subtracted twice??

[@dr.piercesphysicsmath9071]

To complete the square we added and subtracted 9. The +9 helped us complete the square to get (x-3)^2, which is also x^2 -6x +9, and the -9 was combined with the +13 in the example to get +4. We did not subtract 9 twice. I hope that is helpful!

[@jacksonmurray6775]

when you say the roots for factored form do you mean the x intercepts

[@dr.piercesphysicsmath9071]

Yes! 👍

[@MushiSaad1]

Thanks man

[@Keikojourney]

in vertex form x=-3 right

[@dr.piercesphysicsmath9071]

Yep. 3 is the x coordinate of the vertex and x=3 is the vertical line about which the parabola is symmetric. If you plug in other values of x, you'll get other points on the parabola.

[@zianjohnillustrisimo9375]

Can someone explain to me the uses of imaginary roots?

[@dr.piercesphysicsmath9071]

Situations that arise in physics, engineering, math, econ, chem, and bio can lead to exponential behavior (e^kt). If the exponents (k) are imaginary, the system shows oscillatory behavior. If the exponents (k) are real, they show growth or decay. If they are complex (real and imaginary parts) the system shows both oscillation and growth/decay. The process of solving the differential equation can involve solving a quadratic "characteristic equation" for the exponents (k), just as one might solve a quadratic in Algebra 2 in 10th grade (in the US, anyway).

[@abigailb12344]

i have a test tm tysm