1. Section 3.1 Day 2 – Quadratic Functions After this section you should be able to: Graph a quadratic function with and without a calculator. Find the coordinates of two additional points on the parabola. Find the x – intercepts of a quadratic function. Find the quadratic equation, given a graph.

2. (h, k) –vertex V(3, 5)V(-2, -4) a – denotes ‘width’ of the parabola Graph the quadratic function without a calculator.

3. V(4, 2)V(-1, 3) Graph the quadratic function without a calculator. You Try:

4. V(-1, -3) Find the coordinates of two additional points on the parabola. How to obtain two additional points on a parabola (when not given a graph) 1. Identify the vertex (you may need to put the function in standard form in order to find the vertex) 2. Add and subtract 1 to the x-value of the vertex. 3. Plug these new x values into your function and simplify to obtain new y – values. These become your two additional points. *You need these points in order to graph without a calculator.

5. How to obtain the x – intercepts of a quadratic function 1. Keep the equation in general form 2. Enter a 0 in for y, and solve for x to obtain the x - intercepts. List them as ordered pairs (x,y) Find the x – intercepts of a quadratic function On a graph, how do you know where the x – intercept is? What is the y-value for an x – intercept? What are some ways you can solve a quadratic equation? Factoring, Complete the Square, Quadratic Formula You Try: Find the x – intercepts

6. Find the equation of the quadratic function whose graph is below:

8. Extra Practice (on your own) 1. Find the equation of the quadratic function whose graph is below:

9. 2. Find the equation of the quadratic function whose graph is below: Extra Practice (on your own)

10. 3. Review: Identify the vertex of the following parabolas:

11. Extra Practice (on your own) 4. Find the equation of the quadratic function with given vertex and whose graph passes through the given point. a) V(1, 3) Pt: (2, 4)b) V(-2, -5) Pt: (0, 1) c) V(0, 5) Pt: (2, 0)

12. Extra Practice (on your own) 5. Write the quadratic function in standard form. a)b) c) d)

13. Extra Practice: (on your own) 6. Find the coordinates of two additional points on the parabola. Find the vertex and the x – intercepts

14. Section 3.1 Day 2 – Quadratic Functions After this section you should be able to: Homework: Graph a quadratic function with and without a calculator. Find the coordinates of two additional points on the parabola. Homework: On your own practice problems

15. Answers to Extra Practice (on your own) 1. Find the equation of the quadratic function whose graph is below:

16. 2. Find the equation of the quadratic function whose graph is below: Answers to Extra Practice (on your own)

17. 3. Review: Identify the vertex of the following parabolas: V(-1, -3) V(2, 1) V(2, -3) V(-4, -1) V(2, 4) V(-4, -1)

18. Answers to Extra Practice (on your own) 4. Find the equation of the quadratic function with given vertex and whose graph passes through the given point. a) V(1, 3) Pt: (2, 4)b) V(-2, -5) Pt: (0, 1) c) V(0, 5) Pt: (2, 0)

19. Answers to Extra Practice (on your own) 5. Write the quadratic function in standard form. a)b) c)d)

20. Answers to Extra Practice: (on your own) 6. Find the coordinates of two additional points on the parabola. Find the x – intercepts V(-4, 1) V(2, 3) Since there are no real solutions (only imaginary), the parabola will not intersect the x – axis (*Try putting it into your calc. to see what graph looks like) No Real Number Solution – No x-intercepts