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