Put the following functions into standard form by completing the square. Use proper notation throughout.

Question

 

f(x)=3x²+x-10

 

I dont know what goes next after these two steps:

 3(x²+1/3x+(1/6)²-1/36)-10

 3((x+1/6)²-1/36)-10

                                                                        

Answer 1

f (x) = a(x - h)² + k, where (h, k) is the vertex of the parabola

 

f(x) = 3x² + x - 10

 

y = 3x² + x - 10

 

y = 3[x² + (1/3)x - 10/3] 

 

y/3 = x² + (1/3)x - 10/3

 

y/3 + 10/3 = x² + (1/3)x

 

Take half of the coefficient of the x term, 1/3, square it and add to both sides:

(1/2)(1/3) = 1/6  ... (1/6)² = 1/36

 

y/3 + 10/3 + 1/36 = x² + (1/3)x + 1/36

 

y/3 + 120/36 + 1/36 = (x+1/6)²

 

y/3 + 121/36 = (x + 1/6)²

 

y/3 = (x+1/6)² - 121/36

 

y = 3[(x+1/6)² - 121/36]

 

y = 3(x+1/6)² - 121/12

 

f(x) = 3(x+1/6)² - 121/12