Quadratic mindmap

Axis of Symmetry
1. The Axis of Symmetry goes through the vertex
  1. The axis of symmetry is located directly between the roots
2. the dotted red line on this graph is the axis of symmetry
  1. work cited
    1. "Axis of Symmetry of a Parabola." Axis of Symmetry of a Parabola. NCS Pearson, 2014. Web. 10 Sept. 2015. <http://math.tutorcircle.com/analytical-geometry/axis-of-symmetry-of-a-parabola.html>.
      1. "Find Zeros, Vertex, Minimum, Maximum - Integrated Math III." Find Zeros, Vertex, Minimum, Maximum - Integrated Math III. Google Sites. Web. 14 Sept. 2015.
        "End Behavior of a Function." End Behavior of a Function. Hotmath.com. Web. 11 Sept. 2015.
  2. "Axis of Symmetry of a Parabola." Axis of Symmetry of a Parabola. NCS Pearson, 2014. Web. 10 Sept. 2015. <http://math.tutorcircle.com/analytical-geometry/axis-of-symmetry-of-a-parabola.html>.
vertex
1. the vertex can be the minimum of maximum point of a parabola
  1. the vertex is the point where there is a change in the parabola and table
    1. the vertex is shown above
      1. vertex form is y=a(x-h)^2+k
        "Axis of Symmetry of a Parabola." Axis of Symmetry of a Parabola. NCS Pearson, 2014. Web. 10 Sept. 2015. <http://math.tutorcircle.com/analytical-geometry/axis-of-symmetry-of-a-parabola.html>.
parabola
1. a parabola is a graph of a quadratic equation
  1. An arch equal distance from the focus and directrix
    1. Pierce, Rod. "Parabola" Math Is Fun. Ed. Rod Pierce. 8 Oct 2014. 13 Sep 2015 <http://www.mathsisfun.com/geometry/parabola.html>
minimum
1. the lowest point of a parabola
  1. this identifies that the parabola is positive
    1. this can identify the vertex
      1. "Find Zeros, Vertex, Minimum, Maximum - Integrated Math III." Find Zeros, Vertex, Minimum, Maximum - Integrated Math III. Google Sites. Web. 14 Sept. 2015.
maximum
1. The highest point of a parabola
  1. this point means the parabola is negative
    1. Redden, John. "Graphing Parabolas." Graphing Parabolas. Web. 11 Sept. 2015.
y-intercept
1. The point where the parabola crosses the y axis
x- intercept
1. The point where the parabola intersects the x- axis
  1. same as the roots of a quadratic
zeros of the function
1. ax^2+bx^2+cx^2=0
  1. (x+2)(x+2)=0
    1. graph to find the point where the x-value becomes zero
2. the point where the value is equal to zero
  1. ax^2+bx^2+c^2=0
    1. (x+4)(x+3)=0
roots of the equation
1. same as the x intercept the point intersecting the x axis
  1. y=ax^2+bx+c
    1. y=x^2+12x+36
      1. y=(x+6)(x+6)
        roots= x+6=0 x+6=0
        roots= x=-6 x=-6
end behavior
1. the behavior of f(x) with x going towards positive or negative
  1. determined by the coefficent and the number the value is squared by
2. the behavior of f(x) as x approaches positive or negative
  2. "Axis of Symmetry of a Parabola." Axis of Symmetry of a Parabola. NCS Pearson, 2014. Web. 10 Sept. 2015. <http://math.tutorcircle.com/analytical-geometry/axis-of-symmetry-of-a-parabola.html>. Copy & Paste Parenthetical Edit Delete "End Behavior of a Function." End Behavior of a Function. Hotmath.com. Web. 11 Sept. 2015.
discriminant
1. informs you of the roots of a quadratic
differences of squares
1. (a-b)(a+b)
  1. a^2-b^2
2. (a-b)(a+b)
  1. a^2-b^2
factors of a quadratic
1. the binomials multiplied to create a parabola
  1. one form of a quadratic is factored form
    1. ex: (x-5)(x+21)
2. The binomials multiplied to create a parabola
  1. factored form
    1. (x-3)(x+12)
perfect square trinomial
1. Multiplying a binomial by itself twice
  1. (a + b)^2
    1. This can be seen in two factors that are the same
2. a binomial multiplied by itself twice
  1. (x-2)^2

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