Another blog

Aim: How do we calculate quadratic inequalities?

Hi :) again, another math blog.

what are quadratic inequalities?
quadratic inequalities are similar to quadratic equations the only difference is the inequality signs are added.

A sample of a quadratic inequality is :
x2+10x+25≤ 0

lets use this quadratic inequality to solve it :

STEP 1: Foil the quadratic inequality as a quadratic equation.

x2+10x+24 =  (x+6)(x+4)

STEP 2: Find  X by equaling the expressions to zero.

     x+6=0                                              x+4=0
        -6=-6                                               -4=-4
         x=-6                                                x=-4

STEP 3: Plot points back to the equation to know what way the arrow will be going.

Ex: (0,0)
0^2+10(0)+24 ≤ 0
0+0+24≤ 0
24 ≤ 0

This is not true because 24 is greater than 4, therefore the (-4) will not go in the direction that the zero is at.

Ex: (-10,0)
-10^2+10(-10)+24 ≤ 0
100+(-100)+24≤ 0
 24≤ 0

Because 24 is greater than 0 the closest number to -10 ,(-6) will not go in the direction of -10. 

With the new found information we will now use it and correctly plot the points in a graph.

STEP 4: GRAPH 
(Remember )
≤   Less than or equal to signs have a closed circle when graphed.

YOU TRY NOW :

1.

Using a number line,  graph the solution set of

2.

Solve algebraically:

Works Cited:

Regents prep Problems: http://www.regentsprep.org/Regents/math/algtrig/ATE6/quadinequalpractice.htm

Graph pic: It was made by me