Quadratic function

Question

Write the quadratic function in the form. F(x)=a(x-h)^2+k

 

Then, give the vertex of its graph.

 

f(x)=3x^2+12x+13

Answer 1

y = 3x^2 + 12 x + 13

 

  = 3(x^2 + 4x)  + 13 <-- factors out 3 

 

  = 3(x^2 + 4x + 4) + 13 - 12 <-- completes the square; 

 

  = 3(x+2)^2 + 1

 

(-2,1) is the vertex