Question

2x2−8x+14 rewrite in vertex form

Answer 1

2(x -2)² +6

Explanation:

You want the quadratic 2x² -8x +14 written in vertex form.

Vertex form

The vertex form of a quadratic is ...

y = a(x -h)² +k

where the vertex is (h, k) and 'a' is the leading coefficient.

It is often useful to start by factoring the leading coefficient from the variable terms:

=2(x² -4x) +14

Now we add inside parentheses a value that is the square of half the x-coefficient. The same value is subtracted outside parentheses.

= 2(x² -4x +(-4/2)²) +14 -2(-4/2)²

= 2(x² -4x +4) +14 -2(4)

= 2(x -2)² +6