Section 4.7: Completing the Square

The trinomial x2 – 8x + 16 is a perfect square because it equals (x – 4)2. Sometimes you need to add a term to an expression x2 + bx to make it a square. This process is called completing the square.

Completing the Square To complete the square for the expression x2 + bx, add . Diagram on pg. 284

Completing the Square In each diagram, the combined area of the shaded regions is x2 + bx. Adding completes the square in the second diagram.

The method of completing the square can be used to solve any quadratic equation. When you complete a square as part of solving an equation, you must add the same number to both sides of the equation.

Example 1: Solve

Example 2: Find the value of c that makes a perfect square trinomial Example 2: Find the value of c that makes a perfect square trinomial. Then write the expression as the square of a trinomial.

Example 3: Solve by completing the square.

Example 4: Solve by completing the square.

HOMEWORK (Day 1) pg. 288; 8 – 26 even

Example 5: The area of the triangle shown is 144 square units Example 5: The area of the triangle shown is 144 square units. What is the value of x? 2x x + 10

Recall from section 4.2 that the vertex form of a quadratic function is y = a(x – h)2 + k where (h, k) is the vertex of the function’s graph. To write a quadratic function in vertex form, use completing the square.

Example 6: Write in vertex form. Then identify the vertex.

Example 7: The height y (in feet) of a ball that was thrown up in the air from the roof of a building after t seconds is given by the function y = -16t2 +64t + 50. Find the maximum height of the ball.

HOMEWORK (Day 2) pg. 288 – 289; 28 – 38 even, 42 – 48 even