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