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