Shifting the Standard Parabola
Graphs of Quadratic Functions
If a is positive, then our parabola
opens up.
If a is negative, then our parabola
opens down.
y = ax2 + bx + c
The Standard ParabolaThe Graph of the Quadratic Equation
y = x2
Shifting the Standard Parabola
Graphing y = x2 + 1
Standard Parabola y = x2
y = x2 + 1 shifts the standard parabola UP 1
Shifting the Standard Parabola Graphing y = x2 - 3
Standard Parabola y = x2
y = x2 - 3 shifts the standard parabola
DOWN 3
Shifting the Standard Parabola
Standard Parabola y = x2
y = -x2
Flips the u-shape
!
Shifting the Standard Parabola Graphing y = 2x2
Standard Parabola y = x2
y = 2x2
Narrows the u-shape
!
Shifting the Standard Parabola Graphing y = 2x2
Standard Parabola y = x2
y = 2x2
Narrows the u-shape
Shifting the Standard Parabola Graphing y = ½x2
Standard Parabola y = x2
y = ½x2
Widens the u-shape
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
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