1. Do Now 1.Factor: f(x) = 3x 2 + 10x + 8 2.Factor f(x) = 2x 2 - 7x + 3

2. Today’s Question: How do you graph quadratic functions in vertex form? What important characteristics do you see in the vertex form?

3. Standard Form 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:

4. Let’s Review What is the Vertex? The lowest or highest point of a parabola. Vertex What is the Axis of Symmetry? The vertical line through the vertex of the parabola. Axis of Symmetry

5. 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!)

6. Vertex Form  Every function 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

7. Example 1: Graph y = (x + 2) 2 + 1 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 the Step 4 Use symmetry to complete the graph, or find two points on the left side of the vertex. left side of the vertex.

8. With a partner: Find the key characteristics: f(x) = -.5(x+3) 2 +4 Does parabola open up of down? Does parabola open up of down? Vertex is (h,k) Vertex is (h,k) Axis of symmetry x = Axis of symmetry x = Table of values x y Table of values x y -1 2 -1 2 -2 3.5 -2 3.5 -3 4 -3 4 -4 3.5 -4 3.5 -5 2 -5 2 Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

9. Now you try one!

11. Changing from vertex or intercepts form to standard form The key is to FOIL! (first, outside, inside, last) The key is to FOIL! (first, outside, inside, last) Ex: y=-(x+4)(x-9)Ex: y=3(x-1) 2 +8 Ex: y=-(x+4)(x-9)Ex: y=3(x-1) 2 +8 =-(x 2 -9x+4x-36) =3(x-1)(x-1)+8 =-(x 2 -9x+4x-36) =3(x-1)(x-1)+8 =-(x 2 -5x-36) =3(x 2 -x-x+1)+8 =-(x 2 -5x-36) =3(x 2 -x-x+1)+8 y=-x 2 +5x+36 =3(x 2 -2x+1)+8 =3x 2 -6x+3+8 =3x 2 -6x+3+8 y=3x 2 -6x+11 y=3x 2 -6x+11

12. Converting from standard to vertex fom http://www.virtualnerd.com/ algebra-2/quadratics/solve- by-completing-square- roots/complete- square/completing-square- convert-standard-to-vertex

13. Challenge Problem Write the equation of the graph in vertex form. Write the equation of the graph in vertex form.

14. (-1,0)(3,0) (1,-8) x=1