Example 2 -Vertex Formula

a) y = 2x^2+4x 

1. 1. we get the a, b, c in the formula y = ax^2 + bx + c

      • a = 2

      • b = 4

      • c = 0

   2. then we plug in a, b into the formula

      • x = -b / (2a)

      • x = -4 / (2*2) = -4/4 = -1

• so the axis of symmetry is x = -1

• to find the vertex

• so the known vertex data is  (-1, y)

• to find y for the vertex we need to plug -1 into the formula y = 2x^2+4x 

• y = 2*-1^2+4*-1 = -6

• so the vertex is (-1, -6)

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B) y = -x^2 + 4x - 5 

1. 1. we get the a, b, c in the formula y = ax^2 + bx + c

      • a = -1

      • b = 4

      • c = -5
        

   2. then we plug in a, b into the formula

      • x = -b / (2a)

      • x = -4 / (2*-1) = -4/-2 = 2
        

• so the axis of symmetry is x = 2

• to find the vertex

• so the known vertex data is  (2, y)

• to find y for the vertex we need to plug -1 into the formula y = 2x^2+4x 

• y = -2^2 + 4 * 2 - 5 = -1
  

• so the vertex is (2, -1)