This lesson is all about Quadratic Polynomials in standard form.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Finding the degree of a polynomial is nothing more than locating the largest exponent on a variable. So, this means that a Quadratic Polynomial has a degree of 2!
This lesson is all about analyzing some really cool features that the Quadratic Polynomial Function has:
- axis of symmetry
- vertex
- real zeros
just to name a few.
We will begin with a quick review of how to identify the degree of a Polynomial Function and also its leading coefficient. They hold the key to what the graph is going to look like!
Next, we will learn how to identify the y-intercept, axis of symmetry, vertex, the number of zeros, concavity, and also end behavior.
Graph of Quadratic Polynomial
Wait!
What do you mean by Axis of Symmetry? Vertex? Zeros? Concavity? and End Behavior?
Great questions!
Okay, so haven’t you ever noticed that Quadratic Functions look like mirror images of each other if you just cut it right down the middle? In essence, it looks symmetrical.
Well, as Virtual Nerd nicely points out, this is called the Axis of Symmetry, and it is found at the vertex of a parabola.
Now, the Vertex of a Quadratic Polynomial is what is referred to as its turning point. In other words, it’s the maximum or minimum value of our parabola.
Zeros are what mathematicians like to call x-intercepts! They are also sometimes referred to as Roots or Solutions.
And, Concavity, is nothing more than how the graph opens. Does it open up? or does it open down?
Lastly, the End Behavior of a polynomial is the behavior of the graph as it approaches positive or negative infinity. In other words, what is the graph doing as we get further and further away from zero?
Together, we are going to become Quadratic Polynomial masters!
Quadratic Polynomials Explained – Video
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