Quadratic mindmap

Quadratic mindmap

1. Axis of Symmetry

   • The Axis of Symmetry goes through the vertex
     • The axis of symmetry is located directly between the roots
   • the dotted red line on this graph is the axis of symmetry
     • work cited
       • "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>.
         • "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.
     • "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>.

2. vertex

   • the vertex can be the minimum of maximum point of a parabola
     • the vertex is the point where there is a change in the parabola and table
       • the vertex is shown above
         • 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>.

3. parabola

   • a parabola is a graph of a quadratic equation
     • An arch equal distance from the focus and directrix
       • Pierce, Rod. "Parabola" Math Is Fun. Ed. Rod Pierce. 8 Oct 2014. 13 Sep 2015 <http://www.mathsisfun.com/geometry/parabola.html>

4. minimum

   • the lowest point of a parabola
     • this identifies that the parabola is positive
       • this can identify the vertex
         • "Find Zeros, Vertex, Minimum, Maximum - Integrated Math III." Find Zeros, Vertex, Minimum, Maximum - Integrated Math III. Google Sites. Web. 14 Sept. 2015.

5. maximum

   • The highest point of a parabola
     • this point means the parabola is negative
       • Redden, John. "Graphing Parabolas." Graphing Parabolas. Web. 11 Sept. 2015.

6. y-intercept

   • The point where the parabola crosses the y axis

7. x- intercept

   • The point where the parabola intersects the x- axis
     • same as the roots of a quadratic

8. zeros of the function

   • ax^2+bx^2+cx^2=0
     • (x+2)(x+2)=0
       • graph to find the point where the x-value becomes zero
   • the point where the value is equal to zero
     • ax^2+bx^2+c^2=0
       • (x+4)(x+3)=0

9. roots of the equation

   • same as the x intercept the point intersecting the x axis
     • y=ax^2+bx+c
       • y=x^2+12x+36
         • y=(x+6)(x+6)
           • roots= x+6=0 x+6=0
             • roots= x=-6 x=-6

10. end behavior

    • the behavior of f(x) with x going towards positive or negative
      • determined by the coefficent and the number the value is squared by
    • the behavior of f(x) as x approaches positive or negative
      • "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.

11. discriminant

    • informs you of the roots of a quadratic

12. differences of squares

    • (a-b)(a+b)
      • a^2-b^2
    • (a-b)(a+b)
      • a^2-b^2

13. factors of a quadratic

    • the binomials multiplied to create a parabola
      • one form of a quadratic is factored form
        • ex: (x-5)(x+21)
    • The binomials multiplied to create a parabola
      • factored form
        • (x-3)(x+12)

14. perfect square trinomial

    • Multiplying a binomial by itself twice
      • (a + b)^2
        • This can be seen in two factors that are the same
    • a binomial multiplied by itself twice
      • (x-2)^2

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