Express f in standard form - precalculus question

Question

I'm having a lot of difficulty with this problem because I can't find out how to write it in standard form because I don't know how to complete the square. Any help would be greatly appreciated!

 

A quadratic function f is given.

f(x) = 3x2 + 2x − 2

(a) Express f in standard form.

(b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.) 

Answer 1

f(x) = 3x² + 2x − 2

 

y    = 3x² + 2x − 2

 

y+2 = 3(x² + (3/2)x     )

 

now develop constant term to be inserted before the terminal parenthesis, which is the square of half of the coefficient of x, i.e (¾)² -- this will be 9/16. HOWEVER, DOING THAT INSERTION ACTUALLY ADDS 27/16 TO THE RIGHT SIDE BECAUSE OF THE FACTORED-OUT 3. THEREFORE OUR NEXT VERSION OF THIS EQUATION IS:

 

y+2 + 27/16  = 3(x² + (3/2)x + 9/16 )

 

The right side is now 3(x + ¾)²

 

You will now finish the job by combining the constants on the left side of the equation and removing that improper fraction to the right side of the equation, where of course it takes on a negative sign.