1. 3.1 Quadratic Functions and Models

2. A quadratic function is a function of the form:

3. Properties of the Graph of a Quadratic Function
Parabola opens up if a > 0; the vertex is a minimum point.
Parabola opens down if a < 0; the vertex is a maximum point.

4. Graphs of a quadratic function f(x) = ax2 + bx + c
Vertex is highest point
Axis of symmetry
Axis of symmetry
a > 0
a < 0
Opens up
Opens down
Vertex is lowest point

5. Steps for Graphing a Quadratic Function by Hand
Determine the vertex.
Determine the axis of symmetry.
Determine the y-intercept, f(0).
Determine how many x-intercepts the graph has.
If there are no x-intercepts determine another point from the y-intercept using the axis of symmetry.
Graph.

6. Since -3 < 0 the parabola opens down.
Without graphing, locate the vertex and find the axis of symmetry of the following parabola. Does it open up or down?
Vertex:
Since -3 < 0 the parabola opens down.

7. Finding the vertex by completing the square:

8. (2,4)
(0,0)

9. (0,0)
(2, -12)

10. (2, 0)
(4, -12)

11. Vertex
(2, 13)

12. Determine whether the graph opens up or down.
Find its vertex, axis of symmetry, y-intercept, x-intercept.
x-coordinate of vertex:
y-coordinate of vertex:
Axis of symmetry:

13. There are two x-intercepts:

14. (0, 5)
(-5.55, 0)
(-0.45, 0)
Vertex: (-3, -13)