Question

given the quadratic function y = x² - 2x -3 and y = -x² + 4x - 1, transform them into the form y = a(x - h) ² + k.


y=x²-2x-3 y=-x² + 4x-1​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

vertex of parabola/graph of quadratic equation = (h,k)

h = -b/2a

k = 4ac - b²

       4a

1) y = x² - 2x - 3

  a = 1;   b = -2;   c= -3

   h = -(-2)/ 2(1)

   h = 2/2

   h = 1

   

   k = 4ac - b²

             4a

   k = 4(1)(-3) - (-2)²

            4(1)

   k = - 12 - 4

           4

   k = -16/4

   k = - 4

   

  Vertex form : a (x-h)² + k,  substitute the values for h and k:

  Vertex form: a(x-1)² - 4

2) -x² + 4x-1

  a = -1;   b = 4;    c= -1

   

 h = -(4)/2(-1)

 h = -4/-2

 h = 2

   

 k = 4(-1)(-1) - (4)²

           4(-1)

 k = 4 - 16

         -4

 k = -12/-4

 k = 3

 

 Vertex form:  Substitute the values for h and k:

 Vertex form:  - (x-2)² + 3

Step-by-step explanation: