1. Warm UP Domain All real numbers Range y ≥ -6 Equation y = x² - 6
Interval of Increase
0 ≤ x ≤ ∞

2. Quadratic Form to Form
Notes

3. Change quadratic functions to standard form
Rewrite (x+1)²
Multiply using FOIL
Don’t forget your +2
Combine like terms
Standard Form

4. Compare Vertex vs. Standard
Standard form:
Vertex form:
Lets look at our last problem
We converted to
a = 1
b = 2
c = 3
a = 1
h = -1
k = 2
Compare values
You will learn that you will need to identify the values for a, b, and c. Lets get into the habit of identifying them NOW!!

5. Lets try this one! Y = -x² -6x -8
Write the quadratic function in standard form. Label the values for a, b, and c.
Y=-(x+3)(x+3) + 1
Steps:
Write (x+3) twice
Multiply using Foil
Distribute the negative
Add the 1 and combine like terms.
Y = -(x² +6x +9) +1
Y= -x² -6x -9 +1
Y = -x² -6x -8

6. Your Turn
Write the quadratic function in standard form. Label the values for a, b, and c.
Steps:
Write ( ) twice
Mulitply using Foil
Distribute number out front
Combine like terms.

7. Standard to Vertex a x y Step 1: Find x value
Step 2: Plug x back into equation to get y value
Step 3: change the value of your x
Vertex: (-2, -4)
Step 4: “a” from standard form is the same “a” in vertex form a x y

8. Intercept Form Change to standard form Y = -2(x-2)(x+3) Steps
1. FOIL out the ( )
Y = -2 (x² +3x -2x -6)
2. Collect like terms
Y = -2(x² +1x – 6)
3. Distribute
Y = -2x² -2x +12
Make sure equation is in y = ax² +bx + c

9. CLASSWORK/HOMEWORK
page 66 (25-27)
Problems on Agenda

10. Practice Change into Standard form
Y = 2(x-4)² + 5 Form? Vertex (4, 5) FOIL y = 2(x-4)(x-4) y = 2(x² -4x -4x + 16) Collect like terms y = 2(x² -8x + 16) Distribute y = 2x² - 16x + 32

11. Practice Change into standard form
Y = 2(x-3)(x+4) Form? Intercept x = 3 x=-4 FOIL y = 2(x² +4x -3x -12) Collect like terms y= 2(x² + 1x -12) Distribute y = 2x² + 2x -24