Assignment, pencil, red pen, highlighter, GP notebook, calculator U4D5 Have out: Bellwork: Rewrite the equations in vertex form by completing the square. Identify the vertex. 1) f(x) = x2 + 4x + 10 2) f(x) = x2 – 8x + 1 3) f(x) = x2 – 6x – 2 total:

( )2 ( )2 ( )2 = (2)2 = 4 = (-4)2 = 16 = (-3)2 = 9 total: 2) f(x) = x2 – 8x + 1 1) f(x) = x2 + 4x + 10 +1 f(x) = (x2 + 4x ____) + 10 ____ + 4 – 4 +1 f(x) = (x2 – 8x ____) + 1 ____ + 16 – 16 ( )2 = (2)2 = 4 ( )2 = (-4)2 = 16 f(x) = (x ____)2 + 10 – 4 + 2 +1 f(x) = (x ____)2 + 1 – 16 – 4 +1 f(x) = (x + 2)2 + 6 +1 f(x) = (x – 4)2 – 15 +1 (–2, 6) (4, –15) +1 +1 3) f(x) = x2 – 6x – 2 f(x) = (x2 – 6x ____) – 2 ____ + 9 – 9 +1 +1 ( )2 f(x) = (x – 3)2 – 11 = (-3)2 = 9 total: (3, –11) +1 +1 f(x) = (x ____)2 – 2 – 9 – 3

Over the last week, we have discussed 3 different ways to rewrite quadratic equations in vertex (graphing) form. Add the following summary into your notes…

1) Average the roots Add to your notes: Example: f(x) = x2 – 2x – 15 c) Determine the vertex a) Find the roots f(1) = (1)2 – 2(1) – 15 0 = x2 – 2x – 15 f(1) = 1 – 2 – 15 0 = (x + 3)(x – 5) f(1) = – 16 x + 3 = 0 x – 5 = 0 x = –3 x = 5 vertex (1, –16) f(x) = (x – 1)2 – 16 b) Take the average = 1 PRO: Helps find all important information of a parabola CON: long process; works primarily for quadratics that factor

2) The "formula" Add to your notes: Example: = –5 f(x) = x2 + 10x + 7 a = 1 b = 10 c = 7 = –5 Line of symmetry or (x–value of vertex) f(–5) = (–5)2 + 10(–5) +7 f(–5) = 25 – 50 + 7 f(–5) = –18 PRO: Faster; quadratic does not have to factor vertex (–5, –18) f(x) = (x + 5)2 – 18 CON: Somewhat faster than factoring, does not give as much information

3) Complete the Square Add to your notes: PRO: Faster CON: Example: f(x) = x2 + 10x + 7 f(x) = (x2 + 10x ____) + 7 ____ + 25 – 25 f(x) = (x + 5)2 – 18 PRO: Faster CON: Now you have more time to do the chores your mom wants you to complete 

Complete the square for each equation, then determine the vertex. Today is a work day, but let’s go over a few more different cases of completing the square that you will see on the worksheet. Complete the square for each equation, then determine the vertex. When you group the terms together, factor out the largest number. Example #1: f(x) = 3x2 + 24x – 7 f(x) = 3(x2 + 8x ____) – 7 ____ + 16 – 48 We are not just adding 16 to the problem. ( )2 = (4)2 = 16 Redistribute the 3. Therefore, we are really adding: f(x) = 3(x ____)2 – 7 – 48 + 4 3 • 16 = 48 f(x) = 3(x + 4)2 – 55 To balance the equation, we need to subtract 48. (–4, –55)

Complete the square for each equation, then determine the vertex. Example #2: f(x) = –x2 – 4x – 12 We are really just adding –4. + 4 + 4 f(x) = –(x2 + 4x ____) – 12 ____ To balance the equation, we add +4. ( )2 = (2)2 = 4 f(x) = –(x ____)2 – 12 + 4 + 2 f(x) = –(x + 2)2 – 8 (–2, –8)

Finish today's assignment: Day 5 Practice Worksheet

Old Slides

( )2 Completing the Square Worksheet Take out the worksheet Complete the square for each equation, then determine the vertex. Example #1: f(x) = x2 – 10x + 31 + 25 – 25 f(x) = (x2 – 10x ____) + 31 ____ ( )2 = (-5)2 = 25 f(x) = (x ____)2 + 31 – 25 – 5 f(x) = (x – 5)2 + 6 (5, 6)

( )2 Completing the Square Worksheet Take out the worksheet = (2)2 = 4 Complete the square for each equation, then determine the vertex. 13) f(x) = 3x2 + 12x + 9 f(x) = 3(x2 + 4x ____) + 9 ____ + 4 –12 ( )2 = (2)2 = 4 f(x) = 3(x ____)2 + 9 – 12 + 2 f(x) = 3(x + 2)2 – 3 (–2, –3)