Intro to Quadratics...the Parabola

The vertex is at (0, 0)

This parabola opens UP and has a MINIMUM value of 0

The DOMAIN is All Real Numbers

The RANGE is  $y\ge0$  

There is one SOLUTION at x=0

The axis of symmetry is x = 0

The y-intercept is 0

The vertex is at (2, 1)

This parabola opens DOWN and has a MAXIMUM value of 1

The DOMAIN is All Real Numbers

The RANGE is  $y\le1$  

There are 2 SOLUTIONS at (1, 0) and (3, 0)

The axis of symmetry is x = 2

The y-intercept is -3

The vertex is at (3, 4)

This parabola opens UP and has a MINIMUM value of 4

The DOMAIN is All Real Numbers

The RANGE is  $y\ge4$  

There are NO REAL SOLUTIONS

The axis of symmetry is x = 3

The y-intercept is 13

The vertex is at (-4, -2)

This parabola opens DOWN and has a MAXIMUM value of -2

The DOMAIN is All Real Numbers

The RANGE is  $y\le-2$  

There are NO REAL SOLUTIONS

The axis of symmetry is x = -4

The y-intercept is -18

The vertex is at (4, 0)

This parabola opens DOWN and has a MAXIMUM value of 0

The DOMAIN is All Real Numbers

The RANGE is  $y\le0$  

There is 1 solution at (4, 0)

The axis of symmetry is x = 4

The y-intercept is -16

The vertex is at (-2, -6)

This parabola opens UP and has a MINIMUM value of -6

The DOMAIN is All Real Numbers

The RANGE is  $y\ge-6$  

There are 2 solutions at approximately (0.45, 0) and (-4.45, 0)

The axis of symmetry is x = -2

The y-intercept is -2