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Unit 3:Quadratic Relations - Coggle Diagram

- - - - The degree of a function is measured by taking the highest exponent of a variable in the function # )
        
        Based on the degree of a function you can ascertain what kind of relation is created by the function
        
        This function is Linear as the degree of the function is one
        
        This function is Quadratic as the degree of the function is two
        
        This function is Cubic as the degree of the function is 3
    - - Finite differences are measured by counting the changes in the y-value when the change in the x-value is constant. As you can see in this table the x-value is increasing by the same number each time (in this case 1)
        
        Finite differences can be used to determine the degree of a function
        
        If the first differences in y-values are constant (provided x increases by the same amount each time), then the function is Linear. #
        
        If the second differences are constant but not zero (provided x increases by the same amount each time), then the function is Quadratic #
    - - The "a" value of a quadratic relation determines which way the parabola opens.
        
        If the "a" value is negative then the parabola would open downwards as shown in the graph # #
        
        if the "a" value is positive then the parabola would open upwards as shown in the graph # #
  - - - The vertex is the highest or lowest point on a parabola
        
        If the parabola opens upwards then the vertex would be the lowest point on the parabola
        
        If the parabola opens downwards then the vertex would be the highest point on a parabola
    - - The axis of symmetry is a vertical line dividing the parabola into two equal halves. The axis of symmetry also goes through the vertex, so the value of the axis of symmetry is the x-value of the vertex #
    - - The maximum or minimum value is the lowest or highest y-value on a parabola
        
        The maximum/minimum value is also the y-value of the vertex
        
        If a parabola opens downwards, then the highest y-value would be your maximum value
        
        If a parabola opens upwards, then the lowest y-value would be your minimum value
  - - - an equation written in the form y = a(x - r)(x - s)
        
        The zeros or x-intercepts of a quadratic relation written in factored form are r and s
        
        Solving for axis of symmetry
        
        If you are given a quadratic relation in factored form, you can solve for the vertex by substituting the axis of symmetry for x #
        
        If a quadratic relation is written in factored form then the value of the axis of symmetry and can be found by dividing the sum of r + s by 2 (r + s)/2 #
    - - an equation written in the form y = ax^2 + bx +c
        
        If you have a quadratic equation in standard form, then the c-value would be the y-intercept
- - - - The distributive property is a way of multiplying that allows you to expand factored relations # #
        
        FOIL(First Outer Inner Last) - in the photo example, you can see how foil works and how it allows the expansion of factored relations
  - - - Curve of good fit- A curve of good fit is an estimated curve that fits the given data points and estimates
        
        When given a question with a table of values, you create a scatter plot then estimate a curve of good fit. Using the curve of good fit, you can find the zeros for the curve. You can then get a quadratic equation in factored form that represents the table of values you were given
        
        In order to get the quadratic equation in standard form, you need the zeros of the equation as well as an additional point on the curve to solve for a #
  - - - The axis of symmetry for the graph is x = 0 (The line is symmetric about the x-axis) #
      - Both the x and y-intercepts are 0
      - The y-value increases and decreases as the absolute value of the x coordinate increases and decreases
    - - The graph this function produces is not symmetric
      - This graph has an asymptote at x = 0, meaning it has no x - intercept
      - The y-values increase much faster as the x-values increase compared to the y = x^2 graph
      - As x decreases the y-value gets closer to 0 #