4.7 – Complete the Square

4.7 – Complete the Square In lesson 4.5, you solved equations of the form x2 = k by finding the square roots. This method also works if one side of an equation is a perfect square trinomial.

4.7 – Complete the Square Example 1a: Solve x2 – 8x + 16 = 25

4.7 – Complete the Square Example 1b: Solve x2 – 2x + 1 = 144

4.7 – Complete the Square Example 1c: Solve 9x2 – 12x + 4 = -3

4.7 – Complete the Square In the first three examples, the trinomials were perfect squares. Sometimes you need to add a term to an expression x2 + bx to make it a square. This process is called completing the square.

4.7 – Complete the Square

4.7 – Complete the Square Example 2a: Find the value that makes x2 + 16x + c a perfect square trinomial. Then write the expression as the square of a binomial.

4.7 – Complete the Square Example 2b: Find the value that makes x2 + 12x + c a perfect square trinomial. Then write the expression as the square of a binomial.

4.7 – Complete the Square Example 2c: Find the value that makes x2 - 13x + c a perfect square trinomial. Then write the expression as the square of a binomial.

4.7 – Complete the Square Example 3a: Solve x2 – 12x + 4 = 0

4.7 – Complete the Square Example 3b: Solve x2 – 10x + 1 = 0

4.7 – Complete the Square Example 4a: Solve 2x2 + 8x + 14 = 0

4.7 – Complete the Square Example 4b: Solve 3x2 + 12x - 18 = 0

4.7 – Complete the Square Example 4c: Solve 2x2 + 10x +17 = 0

4.7 – Complete the Square Example 5a: Write y = x2 – 10x + 22 in vertex form. Then identify the vertex.

4.7 – Complete the Square Example 5b: Write y = 2x2 + 24x + 25 in vertex form. Then identify the vertex.

4.7 – Complete the Square Example 6: The height y (in feet) of a baseball t seconds after it is hit is given by this function: y = -16t2 + 96t + 3. Find the maximum height of the baseball

4.7 – Complete the Square