#5.7 Completing the Square

• (2-32) even

Aim 2: to rewrite a quadratic eqn in vertex form by completing the square

Sorry, I forgot to teach it in class today so here are the notes. Please copy them and add them to your notes from today.

Write in vertex form:

Example a:

y = x^2 + 6x + 2

move the +2 over a few spaces

y = x^2 + 6x + ? + 2

now complete the square:

y = x^2 + 6x + 9 + 2 - 9

we minus 9 at the end because we want to keep the equation balanced. So, if you add 9 to ONE side, you must also minus 9 on the SAME side to keep the equation the balanced.

now factor the perfect square trinomial of x^2 + 6x + 9 and calculate 2-9 for a final answer of:

y = (x+3)^2 - 7

Now, if I wanted to, I could take this one step further and ask you to identify the vertex which would be:

the vertex is at (-3, -7)

Example b:

y = x^2 - 10x - 2

move the -2 over a few spaces

y = x^2 -10x ? - 2

now complete the square:

y = x^2 - 10x + 25 - 2 - 25

we minus 25 at the end because we want to keep the equation balanced. So, if you add 25 to ONE side, you must also minus 25 on the SAME side to keep the equation the balanced.

now factor the perfect square trinomial of x^2 - 10x + 25 and calculate -2-25 for a final answer of:

y = (x-5)^2 - 27

Now, if I wanted to, I could take this one step further and ask you to identify the vertex which would be:

the vertex is at (5, -27)

5 extra credit points to the first person to correctly post a solution/explanattion to a problem. since there are 16 problems for HW tonight, 16 students will be receiving extra credit.