530,134 views
19 votes
19 votes
The equation of the parabola y equals 2 x squared plus 12 x plus 17 in vertex form is ___________.

User Dan Brooke
by
3.3k points

2 Answers

14 votes
14 votes

Answer:

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)

User Rob DiMarco
by
3.0k points
12 votes
12 votes

Answer:

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

User Bardiir
by
3.0k points