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
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