Day: November 19, 2018

Week 10 – Precalc

rubeng2016 on

This week we learned how to solve a quadratic inequality.

example: x^2-x-12\leqslant{0}

The first step would be to rearrange the inequality but in this case, it is not necessary.

so you would the factor the equation

(x-4)(x+3)

 

x=4 x=-3

The next step is to choose a number to use as a test point to determine which section of the graph satisfies the inequality

(-4)^2-(-4)-12\leqslant{0}

 

16+4-12\leqslant{0}

 

8\leqslant{0}

This is not true so it does not satisfy the inequality

Then test another point between -3 and 4, 0 will be the number that is used

0^2-0-12\leqslant{0}

 

-12\leqslant{0}

this is true so it satisfies the inequality

lastly, you have to test a point that is greater than or equal to 4, we will use 5

5^2-5-12\leqslant{0}

 

8\leqslant{0}

this is not true therefore it does not satisfy the inequality. This means that the only solution is -3\leqslant{x}\leqslant{4}