Question

The equation of the parabola y equals 2 x squared plus 12 x plus 17 in vertex form is ___________.

Answer 1

Rewrite the equation in vertex form.

`{y = 2(x+3)^(2)}-1`

Use the vertex from,
`{y = a(x-h)^(2) + k`, to determine the values of
`{a, h, }` and
`k`

`a = 2\\h = -3\\k = -1`

Find the vertex
`(h, k).`

`(-3, -1)`

Answer 2

y = 2(x +3)² -1

Explanation:

You want the vertex form of the equation y = 2x² +12x +17.

Vertex form

The vertex form of the equation is ...

y = a(x -h)² +k² . . . . . . where (h, k) is the vertex and 'a' is a scale factor

Conversion

The equation can be converted to vertex form by the following steps.

1. factor the leading coefficient from the variable terms:
   2(x²+6x)+17
2. add the square of half the x-coefficient inside parentheses:
   2(x² +6x +9) +...
3. and subtract the same amount outside parentheses:
   2(x² +6x +9) +17 -18
4. simplify to vertex form: 2(x +3)² -1

The equation you want is ...

y = 2(x +3)² -1