Lessons in any basic subject up to the high school level. -Starting with Math and Chemistry, but I can help in anything else... probably xD
Spanish notes incoming
This lesson looks confusing, so I figured I should show it.
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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:
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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.
