1. Warm Up

2. CCGPS Geometry Day 37 (9-27-13) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: How do we graph quadratic functions in vertex form? Standard: MCC9-12.F.BF.3

3. 3.2 Graphing Quadratic Functions in Vertex Form Graphing Using Transformations Graphing Using Transformations Domain and Range of Quadratics Domain and Range of Quadratics

4. Quadratic Function A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. Example quadratic equation:

5. Vertex- The lowest or highest point of a parabola. Vertex Axis of symmetry- The vertical line through the vertex of the parabola. Axis of Symmetry

6. Vertex Form Equation y=a(x-h)2+k If a is positive, parabola opens up If a is negative, parabola opens down. The vertex is the point (h,k). The axis of symmetry is the vertical line x=h. Don’t forget about 2 points on either side of the vertex! (5 points total!)

7. Vertex Form  Each function we just looked at can be written in the form (x – h) 2 + k, where (h, k) is the vertex of the parabola, and x = h is its axis of symmetry.  (x – h) 2 + k – vertex form EquationVertex Axis of Symmetry y = x 2 or y = (x – 0) 2 + 0 (0, 0) x = 0 y = x 2 + 2 or y = (x – 0) 2 + 2 (0, 2) x = 0 y = (x – 3) 2 or y = (x – 3) 2 + 0 (3, 0) x = 3

8. Example 1: Graph Analyze y = (x + 2) 2 + 1. Analyze y = (x + 2) 2 + 1. Step 1 Plot the vertex (-2, 1) Step 1 Plot the vertex (-2, 1) Step 2 Draw the axis of symmetry, x = -2. Step 2 Draw the axis of symmetry, x = -2. Step 3 Find and plot two points on one side, such as (-1, 2) and (0, 5). Step 3 Find and plot two points on one side, such as (-1, 2) and (0, 5). Step 4 Use symmetry to complete the graph, or find two points on Step 4 Use symmetry to complete the graph, or find two points on the left side of the vertex. the left side of the vertex.

9. Characteristics Graph y = -(x - 3) 2 + 2. Graph y = -(x - 3) 2 + 2. Domain: Domain: Range: Range:

10. Characteristics Graph y = 2(x + 1) 2 + 3. Graph y = 2(x + 1) 2 + 3. Domain: Domain: Range: Range:

11. Assignment Practice Worksheet