Quadratic Inequalities

“Belong” Game

• Students number off 1-4.

• Look at the group of 4 things. Evaluate items to decide if your number “belongs”. Write Yes or No because _____________ to justify your choice (independently).

• Discuss with small group.

• Share with whole class.

Does it belong? Group A

1 2

3 4

Thoughts?

•Not blue

•Not start with letter “b”

•Living vs. Non-living

Does it belong? Group B

-4 +8 > 6 – 9 = 0 + 5 < 8 + 3 -10 < 3

1 2

3 4

Thoughts?

•Equation

•Linear, not Quadratic

•Had a Greatest Common Factor

Does it belong? Group C

+ 2 > 7 – +2 > 0 + 5 < 2 - 4 < 3

1 2

3 4

Thoughts?

•Trinomial

•Underline Inequality “less than or equal”

•Standard Form + + c

InequalitiesSymbol Words Line Circle

 >  greater than Dashed

- - - - - -

Open

 <  less than Dashed

- - - - - -

Open

 >  greater than or equal

Solid Closed

 <  less than or equal

Solid Closed

Solving Inequalities Notes

Step #1: Find Vertex

Step #2: Find which way parabola opens

Step #3: Find y-intercept (and symmetrical point)

Step #4: Sketch the parabola (solid or dashed?)

Step #5: Shade above or below the parabola.

−𝑏2𝑎

at “A”

at “C”

~Try It~

Step #1: Find Vertex

Step #2: Find Direction

Step #3: Find y-intercept

Step #4: Sketch

Step #5: Shade

= -4.5

+ + 8 > 0+ + 8 = 12.25

𝑉𝑒𝑟𝑡𝑒𝑥 (−4.5 ,12.25)

Opens UpY-intercept = 8

Symmetrical?Greater=Above

~Try It~

Step #1: Find Vertex

Step #2: Find Direction

Step #3: Find y-intercept

Step #4: Sketch

Step #5: Shade

= 1

– 8 > 0 – 8 = -9 𝑉𝑒𝑟𝑡𝑒𝑥 (1 ,−9)

Opens UP

Y-intercept = -8Symmetrical?Less = Above

~Try It~

Step #1: Find Vertex

Step #2: Find Direction

Step #3: Find y-intercept

Step #4: Sketch

Step #5: Shade

= -.5

+ 6 > 0 + 6 = 5.75

𝑉𝑒𝑟𝑡𝑒𝑥 (− .5 ,5.75)

Opens UP

Y-intercept = 6

Symmetrical?

Greater = Above