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 ushape! 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 nicelyshaped 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

What are Quadratic Functions?

Graphing Quadratic Functions

FOILing and Explanation for FOIL

Solving Quadratic Equations by Taking Square Roots

Solving Quadratic Equations by Factoring

Factoring with Grouping

Solving Quadratic Equations Using the Quadratic Formula

Solving Quadratic Equations by Completing the Square

Finding the Value that Completes the Square

Using and Understanding the Discriminant

Word Problems with Quadratic Equations