Quadratics Mind Map

Quadratics Mind Map

1. Standard Form

   • y = ax^2 + bx + c
   • Quadratic Formula
     • Variables in standard form are used to find exact and/or approximate numbers in the quadratic formula
   • Vertex Form
     • y=a(x-h)^2+k
       • Vertex: (h,k)
       • How to turn into Standard Form
         • Ex y=(x-5)^2+3
           • y=x^2-10x+25+3
             • y=x^2-10+28
       • Completing the Square
         • A way to solve a quadratic equation that is not factorized.
           • Ex. y=x^2-10x+3
             • y=(x^2-10x+25-25)+3
               • y=(x-5)^2-25+3
                 • y=(x-5)^2-22
               • Divide the middle term (-10) by 2, then square it. The squared number (25) is subtracted. Take that number (-25) out of the bracket. Turn the bracket into (x-h)^2. Then add/subtract the numbers that are left ( -25 and 3
     • Tells you the vertex of the parabola. Also gives maximum or minimum.
       • Step Method: Going from the vertex, you go to the left/right 1, then up 1, left/right 1, up 3, left/right 1, up 5...(1 will change if "a" has a value. So it would be 1a
   • Intercept Form
     • y=a(x-r)(x-s)
       • How to turn into Standard form
         • Ex. y=(x-5)(x-6)
           • y=x^2-5x-6x+30
             • y=x^2-11x+30
         • Use Distributive Property
           • y=a( x - r )( x - s )
             • y=ax^2+bx+c
       • How to Factor Standard Form into Intercept Form
         • Ex. y=x^2-11x+30
           • First, you must find what two numbers make "b" and "c". B will be the sum of the two numbers. C will be the product of the two numbers.
           • In this case. The two numbers are -6 and -5.
           • y=(x-5)(x-6)
     • Tells you the x-intercepts of the parabola. Y is 0 for the intercepts

2. Parabolas

   • A parabola consist of x and y intercepts, a vertex, and an axis of symmetry
   • y=x^2

3. Perfect Square Trinomials

   • The product of squaring a binomial
     • Ex. x^2+6x+9 -> (x+3)^2

4. Difference of Squares

   • The sum and difference of two terms
     • Ex. y^2-25 -> (y+5)(y-5)

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