Square Day

Name _____________________________ Date ____________ Period _______
Completing the Square Day 1

For each expression, find the number you would add to make it a perfect square trinomial. Leave fraction answers as improper fractions (no mixed numbers or decimals). Then factor each trinomial.

1. x2 + 10x + _______ 2. y2 – 6y + ¬¬¬¬_______ 3. z2 – 8z + _______

_____________________ _____________________ _____________________ 4. x2 + 12x + _______ 5. x2 – x + _______ 6. x2 + 13x + _______

_____________________ _____________________ _____________________

7. x2 + 11x + _______ 8. _______ 9. _______

_____________________ _____________________ _____________________

For each expression, find
x2 + 4x – 21 = 0 20. x2 – 2x – 48 = 0 21. x2 + 10x – 3 = 0

Solving a Quadratic Equation by Completing the Square
Note: The steps for putting an equation in vertex form [ y = a(x – h)2 + k ] are very similar, except instead of zero on one side of the equation, you’ll have y. And, instead of solving at the end, once you have vertex form you’ll find the vertex of the parabola or the minimum or maximum value (still related to the vertex!).

Equation in x2 + bx + c = 0 form

ex: x2 + 8x – 7 = 0

1. Move the constant, c, to the other side.

ex: x2 + 8x – 7 = 0 + 7 +7 x2 + 8x = 7

2. In order to create a perfect square trinomial on the left side, set up your equation so that you will remember to add to BOTH sides (the equation must stay balanced).

ex: x2 + 8x + = 7 +

3. Calculate what must be added to BOTH sides to create the perfect square trinomial on the left side ( ).

ex: x2 + 8x + = 7 +

4. Add to both sides.

ex: x2 + 8x + 16 = 7 + 16

5. Factor the left side of the equation and simplify the right side.

ex: (x + 4)(x + 4) = 23 (x + 4)2 = 23

6. Solve by taking the square root.

ex:

Equation in ax2 + bx + c = 0