1. Graphing Quadratic Functions and Transformations

2. Properties of Quadratic Functions
Quadratic Functions are U-shaped called a Parabola
Quadratic Functions are Symmetrical about the Axis of Symmetry
Quadratic Functions have a vertex (The vertex is a minimum if it’s the lowest point on the parabola and a maximum if it’s the highest point on the parabola.)
The vertex is ALWAYS located on the Axis of Symmetry

3. Quadratic Function
The equation of a Quadratic function looks like one of the following:
How many times did a linear function touch the x-axis? How many times did the quadratic touch the x axis?

4. Intersecting the x-axis
Linear Functions can only intersect the x-axis 1 time (Unless it’s the function y = 0 and then it intersects the x- axis everywhere because it is on the x-axis)
Since Quadratic Functions are u-shaped. The function can intersect the x-axis 0 times, 1 time, or 2 times.

5. 3 Different Forms of Quadratic Functions
We will discuss these forms in the next few slides.

6. Standard Form The standard form of a quadratic function is
“a” determines if the parabola is opened up or down
The Axis of Symmetry is the vertical line
The vertex is a point (x, y) at
The y intercept is found by putting 0 in for x and solving for y f(0) = y-intercept (in standard form the y-intercept is always the “c” value)
The x-intercepts are found by putting 0 in for y and solving for x. f(x)=0 (In this lesson we will find these using a calculator)

7. Standard Form Example

8. Standard Form Example cont.

9. Standard Form Examples
For more examples: Watch the video embedded in the course under the notes section for this lesson or go to the following links.

10. Vertex Form The vertex form of a quadratic function is
“a” determines of the parabola is opened up of down
The Axis of Symmetry is the vertical line x=h
The vertex is a point (x, y) at ( h , k )
The y intercept is found by putting 0 in for x and solving for y f(0) = y-intercept
The x-intercepts are found by putting 0 in for y and solving for x. f(x)=0 (In this lesson we will find these using a calculator)

11. Vertex Form Example

12. Vertex Form Example cont.

13. Vertex Form Examples
For more examples: Watch the video embedded in the course under the notes section for this lesson or go to the following links.

14. Intercept Form The vertex form of a quadratic function is
“a” determines of the parabola is opened up of down
The Axis of Symmetry is the vertical line that is between the values of x = f and x = g
The vertex is a point (x, y) that is on the axis of symmetry.
The y intercept is found by putting 0 in for x and solving for y f(0) = y-intercept
The x-intercepts are x=f and x=g which will be (f,0) and (g,0)

15. Intercept Form Example

16. Intercept Form Example cont.