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.

[@HowardPilyo]

I really like the explanation ❤

[@ibrahimsuhail6435]

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

[@raptor_xvii9464]

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

[@kagm2730]

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

[@dr.piercesphysicsmath9071]

Terrific! 👍

[@jojotag5344]

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

[@dr.piercesphysicsmath9071]

Excellent. 👍

[@MushiSaad1]

Thanks man

[@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. 👍

[@abigailb12344]

i have a test tm tysm

[@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).