1. Vertex and Axis of Symmetry

2. Graphing Parabolas When graphing a line, we need 2 things: the y- intercept and the slope When graphing a parabola, we need 3 things: the vertex, the axis of symmetry, and 2-3 points The following slides will discuss how we can find the vertex and the axis of symmetry. How we use these components to actually graph the parabola will be discussed in the next lesson.

3. Review Vertex = the point where the two sides of a parabola meet Axis of Symmetry = the vertical line that passes through the vertex and cuts the parabola into two symmetrical parts Quadratic Equations are in the form: y = ax 2 + bx + c

4. Finding the Axis of Symmetry Take the “a” and “b” from the original equation and substitute them into the formula above. (Note: we do not need to use “c” to find the axis of symmetry) The -b means that the sign of “b” changes from whatever it is in the original equation (if it’s positive, it changes to negative and if it’s negative, it changes to positive)

5. Example: Find the axis of symmetry of y = 2x 2 + 8x + 2 Based on the equation, a = 2 b = 8 c = 2 Using the formula, we can substitute in and get: Therefore, the axis of symmetry is the line x = -2.

6. Finding the Vertex Since the axis of symmetry goes through the vertex, once we know the axis of symmetry we know the x-coordinate of the vertex If we know what x is, we can substitute it back into the original equation to find y. See an example (continued from the previous example) on the next slide

7. Example: Find the vertex of y = 2x 2 + 8x + 2 We already determined that the axis of symmetry was the line x = -2. Therefore, we can substitute -2 back into the original equation for x and solve for y. We get: Therefore, the vertex is the point (-2, -6)

8. Maximum vs. Minimum The vertex is either the highest point of the parabola or the lowest point of the parabola. If the parabola opens up (“a” is positive), then the vertex is the lowest point and is called the minimum. If the parabola open down (“a” is negative), then the vertex is the highest point and is called the maximum.

9. Example: Is the vertex of y = 2x 2 + 8x + 2 going to be a maximum or a minimum? According to the equation, a = 2. Since “a” is positive, the parabola is going to open up. Therefore, the vertex would be a minimum.