1. Graphing Parabolas Students will be able to graph parabolas or second degree equations.

2. FHSQuadratic Function2 Quadratic Equations A quadratic equation in x contains an x 2 term and involves no term with a higher power of x. The simplest quadratic equation is: y = x 2 Which of the following are quadratic equation? y = x 3 + 6x 2 y = 4x + 16 y = 55 – x 2 y = 5x 2 – 9x – 1

3. FHSQuadratic Function3 Graphing a Quadratic Equation When you graph a quadratic equation, the graph will be a smooth curve called a parabola. It has a shape like this: The highest point or the lowest point of the parabola is called the vertex. vertex

4. FHSQuadratic Function4 Graph y = x 2 Fill in the table and then graph the points. xy -39 1 00 11 39 After you graph the points draw a smooth curve through the points. The vertex of this parabola is (0, 0)

5. FHSQuadratic Function5 Graph y = – 2x 2 Fill in the table and then graph the points. xy -2-8 00 1 2-8 After you graph the points draw a smooth curve through the points. The vertex of this parabola is (0, 0)

6. FHSQuadratic Function6 Graph y = x 2 – 3 Fill in the table and then graph the points. xy -36 -2 0-3 1-2 36 After you graph the points draw a smooth curve through the points. The vertex of this parabola is (0, -3)

7. FHSQuadratic Function7 Graphing Parabolas As we have seen, some parabolas open upwards and some parabolas open downwards. When the x 2 term is positive, the parabola opens upwards. ( ) When the x 2 term is negative, the parabola opens downwards. ( )