5.5 Completing the Square

Objectives Solve quadratic equations by completing the square. Use completing the square to write quadratic functions in vertex form. Assignment: 23-83 odd

Notice that half of 2 is 1 and (1)(1) = 1

Notice that half of –4 is –2 and (-2)(-2) = 4

Notice that half of –16 is –8 and (-8)(-8) = 64

Each of the trinomials we just looked at factored to a perfect binomial square.

What number would you have to replace c with to make this trinomial a perfect binomial square? 9 Hint: take half of 6 and square it.

What number would you have to replace c with to make this trinomial a perfect binomial square? 49 Hint: take half of –14 and square it. We will call this technique “completing the square.”

Completing the square is a method that lets us solve any quadratic equation. by completing the square.

Solve: 3 3 3 3

Given a quadratic function in standard form you can use completing the square to write it in vertex form to identify the vertex of the graph of the parabola. Standard Form Vertex Form Vertex is (4, -5)

Use completing the square! Vertex (-1, -4)