Originally Posted by

**amy1613** I know my title isn't very descriptive, but there are 3 types of questions i'm in the need of help for. I am very appreciative for any help!

Write the following absolute value expressions as piecewise expressions.

1. |x^2 + x - 12|

I know that it's possible to graph it using my calculator, but is there a way not to use my calculator? Half of calculus is without calculator.

you should already know what y = x^2 + x - 12 looks like ... well, y = |x^2 + x - 12| is the same graph except that the part that is below the x-axis (negative) is reflected to the positive side.

y = x^2 + x - 12 , x __<__ -4 or x __>__ 3

y = -(x^2 + x - 12) , -4 < x < 3

Solve the following by factoring and making the appropriate sign charts. Write your solutions in interval notation.

2. x^2 - 16 > 0

I got (4, ∞) but I don't know what a sign chart is.

x^2 - 16 > 0 ... note that x^2 - 16 = 0 at x = + 4 and x = -4

plot these two numbers on a number line ... it breaks the number line into three sections ...

x < -4 , -4 < x < 4 , and x > 4

take any number in each interval, and "test" it in the original inequality ... if it makes the inequality true, then all values of x in that interval make the inequality true.

you'll see that you forgot the interval (-∞ , -4)

Factor completely.

3. x^2 + 12x + 36 - 9y^2

start with this ... (x + 6)^2 - (3y)^2

help any?