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 NotesStep #1: Find Vertex Step #2: Find which way parabola opensStep #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 DirectionStep #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 DirectionStep #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 DirectionStep #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