1. Chapter 4: Quadratic Functions and Equations
Section 4.1: Quadratic Functions and Transformation

2. Section 4.1: Quadratic Functions and Transformations
Goal: To identify and graph quadratic functions

3. Section 4.1: Quadratic Functions and Transformations
Quadratic Function: a function in the form of :
f(x) = ax2 + bx + c, where a ≠ 0
Parabola: The graph of a quadratic function
Vertex Form: f(x) = a(x – h)2 + k, where a ≠ 0
Vertex of the parabola is (h, k)
Axis of Symmetry: a line that divides the parabola into two mirror images
The axis is located at x = h

4. Section 4.1: Quadratic Functions and Transformations
Parabola:

5. Section 4.1: Quadratic Functions and Transformations
Examples:
Compare the graphs of f(x) = and f(x) = 2x2 by using an x/y chart

6. Section 4.1: Quadratic Functions and Transformations
Minimum Value: the y-coordinate of the vertex if a > 0
Maximum Value: the y-coordinate of the vertex if a < 0

7. Section 4.1: Quadratic Functions and Transformations
You try:
1. Graph f (x) =

8. Section 4.1: Quadratic Functions and Transformations
Translations:

9. Section 4.1: Quadratic Functions and Transformations
You try:
Graph each function. How is each graph a translation of f (x) = x2?
a) g (x) = (x – 3)2 b) h (x) = x2 + 1

10. Section 4.1: Quadratic Functions and Transformations
You try:
3. For y = ½ (x – 3)2 – 5, what are vertex, the axis of symmetry, the minimum or maximum value, the domain, and the range?

11. Section 4.1: Quadratic Functions and Transformations
You try:
4. What is the graph of f (x) = -3 (x + 5)2 + 2?

12. Section 4.1: Quadratic Functions and Transformations
You can use the vertex and a point on the parabola to write the equation of the parabola:
In f (x) = a (x – h)2 + k, plug the vertex in for h and k and any point on the parabola for x and y to find the value of a then write the equation
Example: Write an equation of a parabola if its vertex is (-1, 2) and the point (3, 4) is on the parabola

13. Section 4.1: Quadratic Functions and Transformations
You try:
4. The arch of the Sidney Harbor Bridge is approximately 500 meters long and 85 meters high. What quadratic function models the curve of the arch? Assume the arch starts at (0, 0).

14. Section 4.1: Quadratic Functions and Transformations
Homework:
Pg. 199 #8-36 (even), # 44, 46, (all)