1. Locate Axis of Symmetry & Vertex

2. Standard Form a,b are coefficients (numbers) c is the constant For example, a= 1b= -3c= 6

3. Complete the table: Equation Coefficients Constant a = b = c = y = a = 1 b = 0 c = -6 y = a = -3 b = -4 c = 0

4. Standard Form Example: The axis of symmetry is First, find axis of symmetry:

5. Standard Form *******Substitute the x value into equation to find the y value Finding the Vertex: We found the axis of symmetry is So far, the vertex is at Finally, the vertex is Example continued:

6. Vertex Form Don’t get wrapped up into the equation!! It’s just a guide/hint to help you determine axis of symmetry and the vertex. Here is the formula: Before we analyze the equation, let’s look at some examples of a quadratic function in vertex form

7. Vertex Form Let’s look at some more examples:

8. Vertex Form Are you able to make the connection between the graph and the equation? In other words, we are looking for two pieces of information: axis of symmetry and vertex. Let’s look at the first example again: What is the axis of symmetry? What is the vertex? Determine the connection between your answers and the equation.

9. Vertex Form Here are the next two examples. Explain if your determination is applicable to these examples.

10. Vertex (x, y) Axis of symmetry Maximum/Minimum Example: Vertex (-3, 7) Axis of symmetry x=-3 Maximum/Minimum 7 Vertex Form Recall the definition of vertex.

11. Example: Vertex (8, -2) Example: Vertex (-4, -10) Axis of symmetryMaximum/Minimum Example: Vertex (2, -1) Axis of symmetry x= Maximum/Minimum Example: Vertex (, ) Example: Vertex (3, )

12. Vertex Form Find the axis of symmetry, maximum/minimum, then the vertex. Axis of Symm: Max/Min: Vertex: x = -1 (h, k) -6 (-1, -6) x=h k

13. Vertex Form Find the axis of symmetry, max./min. Axis of Symm: Max/Min: Vertex: x = 4 (h, k) 1 x=h k (4, 1)

14. Vertex Form Find the vertex, axis of symmetry, and maximum/minimum. Axis of Symm: Max/Min: Vertex: x =

15. Vertex Form Find the vertex, axis of symmetry, and maximum/minimum. Vertex: Axis of Symm: Max/Min:

16. Vertex Form Find the vertex, axis of symmetry, and maximum/minimum. Vertex: Axis of Symm: Max/Min:

17. Find the Axis of Symmetry, Vertex, and Max/Min: 1. 4.3. 2. Vertex: Axis of Symm: Max/Min: Vertex: Axis of Symm: Max/Min: Vertex: Axis of Symm: Max/Min: Vertex: Axis of Symm: Max/Min:

18. Vertex Form to Standard Form Now, lets take ANY equation and convert the equation to STANDARD FORM First, recognize if the equation is in standard form: This equation is in standard form because the equation has an a, b and c. What about the next equation? This equation is in standard form because the equation has an a, b and c.

19. Vertex Form to Standard Form Last equation, is this equation in standard form? No, because it has parentheses. So, let’s convert it to standard form: First, expand the parentheses. Next, use the distributive property Now, combine like terms.

20. Vertex Form to Standard Form Try one yourself: