1. Quadratic Functions and Models
Lesson 3.1

2. Nonlinear Data
When the points of the function are plotted, they do not lie in a straight line.
This graph contains points from a quadratic function of the form
Contrast to linear

3. General Form
Quadratic functions have the standard form y = ax2 + bx + c
a, b, and c are constants
a ≠ (why?)
Quadratic functions graph as a parabola

4. Axis of Symmetry Parabolas are symmetric about a vertical axis
For y = ax2 + bx + c the axis of symmetry is at
Given y = 3x2 + 8x
What is the axis of symmetry?

5. Vertex of the Parabola The vertex is the “point” of the parabola
The minimum value
Can also be a maximum
What is the x-value of the vertex?
How can we find the y-value?

6. Vertex of the Parabola Given f(x) = x2 + 2x – 8
What is the x-value of the vertex?
What is the y-value of the vertex?
The vertex is at (-1, -9)

7. Vertex of the Parabola Given f(x) = x2 + 2x – 8
Graph shows vertex at (-1, -9)
Note calculator’s ability to find vertex (minimum or maximum)

8. Other Quadratic Forms Standard form y = ax2 + bx + c
Vertex form y = a (x – h)2 + k
Then (h,k) is the vertex
Given f(x) = x2 + 2x – 8
Change to vertex form
Hint, use completing the square

9. Identifying Quadratic Functions
How can you determine which of the following is quadratic or not?
What determines whether a parabola opens down or up?

10. Modeling Quadratic Data
Consider the following table …
Is it linear or non linear?
Graph the data on your calculator

11. Modeling Quadratic Data
The calculator can do quadratic regression to find a modeling function
While in the data matrix mode
Press F5, then specify QuadReg
Fill in remaining parameters as specified here.

12. Modeling Quadratic Data
Note results
Formula
Graph

13. Assignment Lesson 3.1A Page 168 Exercises 1 – 47 odd Lesson 3.1B