**Video Transcript**

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Transcript
**What are Quadratic Functions?**

*"You've seen the posters. You've seen the billboards. Now drink the drink.
The question of the summer is about to be answered.
The Quadratic Functions are proud to present a refreshing line of new drinks, Parabolica!
Parabolica XTRA Strong is just amazing. It makes gravity work better!"*

*”That jump is a perfectly shaped parabola! What a gorgeous u-shape!
You'll love the extra strong flavor. It’s simply refreshing.
You wanna know Parabolica's secret ingredients? We're gonna tell ya. PARABOLAS!
You may be wondering, is there a standard form like with linear functions? You betcha!”*

A quadratic equation, written in **standard form**, is equal to **y=ax²+bx+c** for all 'a's **not equal to zero**.

*”Wanna be a quadratic function, too? Then the 2nd degree is the way to be!
Tame your inner beast, just look at that beautiful parabola!
Also from quadratic functions: Parabolica Chill! Try it!
Feel the thrill of Parabolica Chill! This drink will give you energy, but not quite so much."*

Back to parabolas and quadratic equations. Let's investigate some **characteristics** of the **equations** and their corresponding **graphs**. The 'a' value, the **coefficient** of the **squared variable**, determines the **width** of the **parabola**. The greater the **'absolute' value** of a, the **thinner** the **parabola**. This is the graph of the quadratic equation, with 'a' = 1: **y = x²**. And this is a graph of a quadratic equation, with 'a' less than 1: **y = (1/2)x²**. And here we have 'a' greater than 1: **y = 6x²**. When we compare to the graph of y = x², it's almost as if were on a diet...

Ok, enough math, back to the energy drinks.

_”Something weighing you down? Try the new Parabolica Lite – you’ll feel light as a feather!
You might even defy gravity!”

*”Will you just take a look at that nicely-shaped parabola?!
See how light he is after drinking Parabolica Lite?
Wanna know another secret about Parabolas?”*

The **sign** of the 'a' value affects a **parabola's direction**. When the 'a' value is negative, the parabola is shaped like a frown. But when the 'a' value is positive, we can turn that frown upside down!

*”Now that we've told you all the secret ingredients for Parabolas"*
Oh dear! It seems they should have invested more money in getting just the right taste - rather than on special effects