Math: "Quadratic Graphs and Their Properties"

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Pictures are not mine.

This lesson looks confusing, so I figured I should show it.

So that looks confusing, right? So let's take a look at the "Essential Understanding"

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So that looks confusing, right? So let's take a look at the "Essential Understanding". It says "A quadratic function is a type of nonlinear function that models certain situations where the rate of change is not constant." This means that the graphs of quadratic functions have a curved line. They look like this:

In this graph, this "symmetric curve" has a "maximum value" or a "highest point

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In this graph, this "symmetric curve" has a "maximum value" or a "highest point."

Onto the key concept, don't be confused by the usage of letters. Remembering the past chapter, you placed polynomials in "standard form." For example:

3x²+4x-5

7p⁵-3p²+2

As you can see, the polynomials are ordered by greatest to lowest degree, or, to put it simply, exponent. Standard form is an order placing the coefficient (3) with a variable with the highest degree (x²) first, followed by the next coefficient/variable with the second highest degree, and finally followed by a constant (-5). (Note: Some polynomials do not have a constant).


So, in the key concept, y=ax²+bx+c, "a" is a coefficient, "x²" is a variable with the highest degree (or ax² is the monomial with the highest degree), "b" is a coefficient, "x" is a variable with the second highest degree (or bx is the monomial with the second highest degree), and "c" is a constant. (Note: a ≠ 0 because then the function would not be a quadratic function.)


Also remembering last lesson, look at the equation for quadratic functions. Notice "ax²". When you wrote the polynomials in standard form, you called them things like "Linear Binomial" or "Cubic Monomial." You also learned that "Quadratic" refers to the Second Degree.

5x²+3x-4             Quadratic Trinomial

2b²+6                  Quadratic Binomial

82n²                    Quadratic Monomial

This is why they are called "Quadratic Functions." That's sort of a useless fact, but it could help you more easily see the difference between different types of functions.


Feel free to ask any questions

Works Cited

1. "12-1 Key Concept." Pearson Realize. Pearson Education, Inc., n.d. Web. 04 Mar. 2017.

2. Terr, David. Quadratic Functions. Digital image. MathAmazement. N.p., n.d. Web. 04 Mar. 2017.

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