1. Quadratic Functions and their Graphs If a graph has an axis of symmetry, then when you fold the graph along this axis, the two halves of the graph coincide. The graph of a quadratic function has a vertical axis of symmetry, or axis. The vertex of the parabola is the point where the axis of symmetry intersects the parabola.

5. To sketch the graph of Decide if it opens up or down and the number of x-intercepts Find the axis and vertex Find the x- and y-intercepts

6. Ex. 1. Sketch the parabola. Label the intercepts, axis of symmetry, and vertex. Does it open up or down? Find the axis To find the vertex, plug in 2 for x and determine the y-coordinate. Find the x and y-intercepts

8. Ex. 2. a.Find the vertex of the parabola by completing the square. b.Find the x- and y-intercepts a. Put in vertex form: where (h, k)is the vertex The vertex is (3, 22)

9. b. When x = 0, y = 4. So the y-intercept is (0, 4) To find the x-intercept, let y = 0

10. Ex. 3. Where does the line y = 3x + 5 intersect the parabola Set and solve for x Substitute these into y = 3x + 5 to get y = -7 and y = 8 So the intersection points are (-4, -7) and (1, 8) Graph to confirm your answer

11. Ex. 4. Find an equation of the function whose graph is a parabola with x-intercepts (3, 0) and (6, 0) and y-intercept (0, -2). If x = 3 and x = 6 are solutions of this equation, then (x – 3) and (x – 6) are factors of the equation so Use the y-intercept Graph to confirm