1. Family of Quadratic Functions
Lesson 5.5a

2. 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

3. Zeros of the Quadratic Zeros are where the function crosses the x-axis
Where y = 0
Consider possible numbers of zeros 
None (or two complex)
One
Two

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. Shifting and Stretching
Start with f(x) = x2
Determine the results of transformations
___ f(x + a) = x2 + 2ax + a2
___ f(x) + a = x2 + a
___ a * f(x) = ax2
___ f(a*x) = a2x2
a) horizontal shift
b) vertical stretch or
squeeze
c) horizontal stretch or
d) vertical shift
e) none of these

9. Geogebra Quadratic Function
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
Experiment with
Geogebra Quadratic Function

10. Vertex Form Changing to vertex form
Add something in to make a perfect square trinomial
Changing to vertex form
Subtract the same amount to keep it even.
This gives us the ordered pair (h,k)
Now create a binomial squared

11. Assignment
Lesson 5.5a
Page 231
Exercises 1 – 25 odd