Complete the square to write the function in f(x) = a(x - h)2 + k form.

Question

Complete the square to write the function in
f(x) = a(x − h)2 + k
form. Determine the vertex and the axis of symmetry of the graph of the function.
f(x) = 2x2 + 12x + 10

 

f(x)=_____________

Answer 1

f(x) = 2x² + 12x + 10

 

f(x) = 2(x² + 6x) + 10

 

f(x) = 2(x² + 6x +(6/2)²) + 10 - 2(6/2)²

 

f(x) = 2(x² + 6x + 9) + 10 - 18

 

f(x) = 2(x+3)² - 8

 

The vertex lies at the point (h,k) = (-3,-8)