Quadratic Inequalities

Multiple Choice

Solve this quadratic equation: $$x^2-x-6=0$$   (Hint: use Desmos!)

• x=+2, -3

• x= -2, +3

• x= -2, -3

• x= +6, -6

Multiple Choice

If this equation was an inequality, $$x^2-x-6<0$$  , what would the solution to the inequality be? (Hint: try using Desmos!)

• $$-2<x<3$$  

• $$x\le6$$  

• $$x<-2$$  and $$x>3$$  

• $$x>3$$  

1 Variable Quadratic Inequalities

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• Our function has zeroes (x-intercepts) when x = −2 or x = +3

• So between −2 and +3, the function will either be

  • always greater than zero, or

  • always less than zero

  We don't know which ... yet!​

​And the answer is...

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​And that is the region we want, so...

x² − x − 6 < 0 in the interval (−2, 3) so -2<x<3

​so -2<x<3

This is what our inequality looks like in Desmos!

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​Quadratic inequalities with only 1 variable do not look like parabolas.

It is similar to a number line question spread across the whole coordinate grid.

Multiple Choice

What is the solution to the inequality $$x^2+2x-8\le0$$  ? (Hint: use Desmos!)

• $$-8<x<2$$   

• $$x<-4$$  

• $$x>2$$  

• $$-4\le x\le2$$  

Multiple Choice

What is the solution to the inequality $$x^2-x-20>0$$  ? (Hint: use Desmos!)

• $$-4<x<5$$  

• $$x<5$$  

• $$x<-4$$   and $$x>5$$  

• $$-4\le x\le5$$  

Multiple Choice

If this equation was an inequality, $$x^2-x-6<0$$  , what would the solution to the inequality be?

• $$-2<x<3$$  

• $$x\le6$$  

• $$x<-2$$  and $$x>3$$  

• $$x>3$$  

Great work! Now for 2 variable Quadratic Inequalities...

Multiple Choice

What is the solution to the inequality $$y<x^2-x-6$$  ? (Hint: use Desmos!)

• Graph parabola

• use solid or dashed line based on symbol

• Shade above or below based on symbol​

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2 variable Quadratic Inequalities

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Multiple Choice

What is the solution to the inequality $$y\le-x^2+4x-1$$  ? (Hint: use Desmos!)

Multiple Choice

What is the solution to the inequality $$y<x^2-x-6$$  ?

Multiple Choice

What is the solution to the inequality $$y>2x^2-4x$$  ?