1. Review: Expand the following (a+b) 2 =a 2 +2ab+b 2 (a-b) 2 =a 2 -2ab+b 2 (a+b) 2 =a 2 +2ab+b 2 (a-b)(a+b)=a 2 -b 2 FOIL Method

2. Questions for thought What is the difference between vertex form and standard form? How do we expand a quadratic from vertex form to standard form?

3. VERTEX FORM TO STANDARD FORM

4. Key definitions The standard form of a quadratic equation is y=ax 2 +bx+c, where a≠0. The y-intercept is c. The direction of opening of parabola and how wide/narrow it is,is determined by a Example: 3x 2 +4x-9 The y-intercept is -9 and a = 3 with no reflection(since a is positive).

5. Example Expand y=3(x-2) 2 +9 Step 1) Expand the binomial: y=3(x-2)(x-2)+9 y=3(x 2 -4x+4)+9 Step2) Multiply the result by 3 (the a value): y=3x 2 -12x+12+9 Step 3) Add the 9 at the end y=3x 2 -12x+21 Therefore, y-intercept is 21

6. Express in standard form (try it yourself) What is the y-intercept of each? -98-10

7. Express in standard form and state the y- intercept (try it yourself) The y-intercept is:The y-intercept is: 27

8. Create an equation based on the given information A parabola opening up with a= 2 and a vertex of (4, 9) y=2(x-4) 2 +9 A parabola has a maximum at (2, 3) with a = 0.5 y=-0.5(x-2) 2 +3 A parabola with a=1, opening down with a vertex at (-3, -4) y=-(x+3) 2 -4

9. Create an equation and express in standard form A parabola opening down with a = 3 and a vertex at (3, 4) The y-intercept is:The y-intercept is: -23