All about Polynomial functions

这是一篇关于All about Polynomial functions的思维导图，主要内容包括：Types of Polynomial Functions，Possible types of end behaviour，Part of Polynomial Functions: Quadratic Functions，Brief explanation of these functions.

All about Polynomial functions

• Necessary steps to remember
  • Even or odd degree: When the highest exponent is odd, it is an odd degree, and when the highest exponent is even, then its an even degree
  • End Behavior: The direction of which the function mainly goes through which ways
  • Leading Coefficient
    • The coefficient with the highest possible exponent in an equation
  • Degree
    • The highest possible exponent in an equation
  • Important methods
    • Even or odd degree: This depends on the degree of a function
    • Domain: The x values in these functions
    • Range: The y values in these functions.
    • These methods we should be careful with
• Possible types of end behaviour
  • Area of application: Necessary to recite the end behaviors, odd and even degrees, and directions of end behaviors and more which does do with how the line can move.
  • Law of end behavior
    • Should represent how the line mainly goes to get the directions of end behaviour
  • When left and right are in the same direction, they arr represented as even degree
    • Both sides going up: This can be represented as even degree with the positive leading coefficient
    • Both sides going down: This is represented as an even degree with the negative leading coefficient
  • When left and right are going two different ways, they are actually represented as odd degree
    • Left going up and right going down: This is represented as odd degree with the positive leading coefficient
    • Left going down and right going up: This is represented as odd degree with the negative leading coefficient
• Examples
  • Practical Index: Helps understanding the techniques of these functions
  • Area of application: Necessary to find these methods easily without having to deal with too much issues.
  • Two important methods
    • Formula Method: Use delta as b^2-4ac and to find the steps afterwards
    • Factorization Method: Use cross multiplication to find the exact result
  • Steps
    • Record all the necessary values
      • Including 7x, 2 and 3 in 7x^2+2x+3
    • Reduce when said about factorizations
      • Including x^2+2x+3 can be factored to (x+2)(x+3)
    • Recite the important values
      • Including coefficients, degree, and more
    • Simplify when explaining about factorizations ‌
      • Including (x-5)(x-3) which should be both equal to zero
    • Review the important variables
      • Including the quadratic variable and the variable with no exponent which is 1
• Types of Polynomial Functions
  • These show the types of polynominal functions including having to deal with the values on these equations.
  • Important things to remember: These are crucial steps to show complete methods
  • Three necessary types of polynomial functions and two necessary values to remember
    • 1. Binomial functions: With two terms in these equations
    • 2. Trinomial functions: With three terms in these equations
    • 3.Monomial functions: With only one term in these equations
    • 4. Degree is the highest value of exponent in any terms with variables.
    • 5. The leading coefficient is the highest value in any terms with the highest value of coefficient.
• Part of Polynomial Functions: Quadratic Functions
  • Meaning of quadratic functions
  • Steps to find out the important equations
  • All about the quadratic coefficient's positive and negative
    • The positive quadratic coefficient means it opens upwards..
    • The negative quadratic coefficient means it opens downwards.
  • Principles of quadratic functions
    • In this function, the degree is a two.
    • The quadratic coefficient should not be equal to zero.
  • All about all the variables in this function
    • The constant variable represents the
    • Please solve like ax^2+bx+c for the main method.
• Brief explanation of these functions
  • Important ideas about the solutions
  • These functions include degree, coefficients, and constants which are necessary to remember.
  • How to solve the entire function in any terms
    • The coefficients are the numbers with variables that should be important to remember.
    • The degree is the highest exponent in any terms with variables in its equation.
  • The four steps of this formula
    • Check out the variables these functions can do.
    • Find out how the equation can do to its functions.
    • See how the lines can deal with the actual solutions.
    • Solve the equation to find out the answers.