# How do you convert the following equation from standard to vertex form by completing the square: #y=3x^2+12x+5#?

##### 1 Answer

Please see the explanation.

#### Explanation:

The given equation is the equation of a parabola that opens upward (or downward). The vertex form of the equation of a parabola that opens upward (or downward) is:

where

Given:

Factor out 3 from the first 3 terms:

Set the middle term in right side of the pattern,

Solve for h:

Substitute the left side of the pattern into the equation:

Substitute -2 for h:

Combine the constant terms:

The above is the vertex form.

The vertex can be read directly from the equation; it is at: