1. Shifting the Standard Parabola

2. Graphs of Quadratic Functions
y = ax2 + bx + c
If a is positive, then our parabola opens up. 
If a is negative, then our parabola opens down. 

3. The Graph of the Quadratic Equation
The Standard Parabola
The Graph of the Quadratic Equation
y = x2

4. Shifting the Standard Parabola shifts the standard parabola UP 1
Graphing y = x2 + 1
y = x2 + 1
shifts the standard parabola UP 1
Standard Parabola y = x2

5. Shifting the Standard Parabola shifts the standard parabola DOWN 3
Graphing y = x2 - 3
y = x2 - 3
shifts the standard parabola DOWN 3
Standard Parabola y = x2

6. Shifting the Standard Parabola!
Shifting the Standard Parabola
y = -x2
Flips the u-shape
Standard Parabola y = x2

7. Shifting the Standard Parabola
Graphing y = 2x2
y = 2x2
Narrows the u-shape
Standard Parabola y = x2
!                                                                                                                            

8. Shifting the Standard Parabola
Graphing y = 2x2
y = 2x2
Narrows the u-shape
Standard Parabola y = x2

9. Shifting the Standard Parabola
Graphing y = ½x2
Standard Parabola y = x2
y = ½x2
Widens the u-shape

10. Shifting the Standard Parabola
y = ax2 + bx + c
when b ≠ 0, changes the x-coordinate of the vertex
 Moving the vertex away from the origin