# What is the vertex form of #7y = 19x^2+18x+42#?

##### 1 Answer

#### Explanation:

Strategy: Use the technique of completing the square to put this equation in vertex form:

The vertex can be pulled from this form as

Step 1. Divide both sides of the equation by 7, to get

Step 2. Factor out

Notice we just multiply each term by the reciprocal to factor it out.

Step 3. Simplify your terms

Step 4. For the term in front of

Term next to

Cut it in half:

Square the result:

Finally, add and subtract that term inside the parenthesis:

The part that can now be expressed as a perfect square is in blue.

This gives you the perfect square using the number you got when you cut it in half (i.e.,

Combine the remaining two fractions inside the parenthesis.

Step 5. Multiply the

ANSWER:

So the vertex is at