Rewrite the quadratic function y = 2x^2 - 16x + 35 in Vertex Form:

Question

A: 2(x - 4)^2 - 3

B: 2(x - 4)^2 + 3

C: 2(x + 4)^2 + 3

D: 2(x + 4)^2 - 3

E: 1/2(x - 4)^2 + 3

Answer 1

Use the Complete the Square Method:

 

y = 2(x² - 8x + 35/2)                      Factored out the 2 before you can start. 

 

y = 2[ (x² - 8x ) + 35/2 ]                 Preparing for complete the square.  Only added brackets to focus on parenthesis

 

y = 2[ (x² - 8x + 16 ) + 35/2 -16 ]   Add and subtract 16.  That is (-8/2)²

y = 2[ (x - 4 )² + 35/2 -16 ]             Substitution  (x2 - 8x + 16 ) = (x-4)(x-4)= ( x - 4 )²

 

y = 2[ (x - 4 )2 + 35/2 - 32/2 ]        Replace 16/1 with 32/2 so you have common denominators.

 

y = 2[ (x - 4 )2 + 3/2 ]                    Subtract fractions.

 

y = 2(x - 4)²  + 3                            Distribute the 2 so you can drop the brackets.  Note: 2(3/2)=3

 

 

You could have used decimals, but if you can get comfortable with fractions, it is actually easier.