![Step 2: Complete the square.
f(x) = a [x2 +bx + (
)2] + c - a(
2
)2
f(x) = a [x2 + bx +(
)2] + c -
2
42
2 2 2](https://image.slidesharecdn.com/quadraticfunctions-copy-140815053210-phpapp01/85/Transforming-Quadratic-functions-from-General-Form-to-Standard-Form-7-320.jpg)
![f(x) = 2 x2 + 5 1 a =2
f(x) = 2(x2 +
5
2
) 1
f(x) = 2[x2 +
5
2
+ (
25
16
)] 1 -
25
8
f(x) = 2(x+
5
4
)2 +(
825
8
)
f(x) = 2(x+
5
4
)2 +(
33
8
)](https://image.slidesharecdn.com/quadraticfunctions-copy-140815053210-phpapp01/85/Transforming-Quadratic-functions-from-General-Form-to-Standard-Form-11-320.jpg)
Transforming Quadratic functions from General Form to Standard Form
- 2. General Form f(x) = ax2 + bx c
- 3. Standard Form f(x) = a (x - k
- 5. STEPS: 1. Factor out a from the first two terms. 2. Complete the square. 3. Factor and combine.
- 6. f(x) = ax2 + bx + c Step 1: Factor out a from the first two terms. f(x) = a (x2 + ) + c
- 7. Step 2: Complete the square. f(x) = a [x2 +bx + ( )2] + c - a( 2 )2 f(x) = a [x2 + bx +( )2] + c - 2 42 2 2 2
- 8. Step 3: Factor and combine. f(x) = a (x + 2 )2 + 42 4 h=- and k = f(x)=a(x-h)2 +k
- 9. Examples
- 10. f(x) = x2 8x + 3 a = 1 f(x) = (x2 8x) +3 f(x) = (x2 8x + ( 8 2 )2) +3 - ( 8 2 )2 f(x) = (x2 8x +(4)2) +3 (4)2 f(x) = (x2 8x +16) +3 16 f(x) = (x 4)2 13
- 11. f(x) = 2 x2 + 5 1 a =2 f(x) = 2(x2 + 5 2 ) 1 f(x) = 2[x2 + 5 2 + ( 25 16 )] 1 - 25 8 f(x) = 2(x+ 5 4 )2 +( 825 8 ) f(x) = 2(x+ 5 4 )2 +( 33 8 )
- 12. 1. f(x) = x2 - 12x + 4 2. f(x) = 5x2 + 20x -12 3. f(x) = x2 + 3x + 36 4. f(x) = 4x2 + 2x + 9 5. f(x) = 3x2 + 6x + 2 Activity Transform the following quadratic functions into standard form.