A is for Algebra

How to complete the square and graph rationals

Completing the Square


Completing the square is a process used to solve for x in a quadratic equation (ax^2 + bx + c = 0). The process is in many cases, quicker than using the quadratic formula. It is especially useful when the cross and box method just doesn't work out (for example, no two integers can both multiply into the top number of the cross, and add into the bottom number).


  1. Move the constant to the right.
  2. Divide by the coefficient if it isn't 1.
  3. Half the B term, then square it ; add this to both sides of the equation.
  4. Write the equation as a perfect square on the left.
  5. Solve.

Graphing Rationals

Background information:

The parent rational function is f(x) = (1/x). This is known as a reciprocal function. A transformation function is f(x) = (a / (x - h)) + k.


  1. Factor.
  2. Solve for denominator (this will be the vertical asymptote).
  3. Find the horizontal asymptote by looking at the three solutions (posted to the right).
  4. Find the slant (if their is one).
  5. Find the zeros.

Example #1:

Example #2:


  • Completing the square is a concept used to factor (and solve for x).
  • Completing the square is good to use when the cross and box method doesn't work out.
  • A rational function is a reciprocal function.
  • The x intercepts in a rational function can be found by solving for X in the numerator.
  1. If P>Q than there is no x intercept (slant)
  2. If P<Q than y=0
  3. If P=Q than y=(3/2)

Upcoming Quizes and Tests:

Tuesday December 8th: Quiz 4

Thursday December 10th: Test 2


McGraw Hill Education textbook (connectedED)