1. Solving Quadratics EQ: How do you solve quadratic inequalities algebraically?
M2 Unit 1C: Day 7

2. To solve quadratic inequalities algebraically:
Change the inequality symbol to =
Get the equation =0
Factor
Solve to get “critical x-values”
Test x-values
State the solution
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3. Solve the inequality algebraically
Pick a number in between the x-intercepts and test to see if that is where the shading should be
Test x = 0:
-3 < 0
TRUE
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4. Solve the inequality algebraically
Pick a number in between the x-intercepts and test to see if that is where the shading should be
Test x = 1.5:
-0.25 > 0
FALSE
x < 1
x > 2
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5. Solve the inequality algebraically
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6. Solve the inequality algebraically
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7. Solve the inequality algebraically
Since
is a "positive" quadratic, the parabola is going up, so I know it goes up forever. For the parabola not to cross the x-axis, it must be that the parabola is always above the axis, as you can see here:
Can’t Factor…so let’s think about it graphically…
So when
is greater than zero (above the axis)? ALWAYS! Then the solution is:
ALL REAL NUMBERS
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8. Think about it this way…
Since
is a "positive" quadratic, the parabola is going up, so I know it goes up forever. For the parabola not to cross the x-axis, it must be that the parabola is always above the axis, as you can see here:
So when
is less than zero (below the axis)? NEVER! Then the solution is:
NO SOLUTION
Can’t Factor…so let’s think about it graphically…
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9. Solve the inequality algebraically
Since
is a “negative" quadratic, the parabola is going down, so I know it goes down forever. For the parabola not to cross the x-axis, it must be that the parabola is always below the axis, as you can see here:
Can’t Factor…so let’s think about it graphically…
So when
is less than zero (below the axis)? ALWAYS! Then the solution is:
ALL REAL NUMBERS
9/21/2019

10. Solve the inequality algebraically
Since
is a “negative" quadratic, the parabola is going down, so I know it goes down forever. For the parabola not to cross the x-axis, it must be that the parabola is always below the axis, as you can see here:
So when
is greater than zero (above the axis)? NEVER! Then the solution is:
NO SOLUTION
Can’t Factor…so let’s think about it graphically…
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11. Assignment: pg 99 (#28–33 all), pg 101 (#23–29 odd)
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