#2**+10 **

I would consider the graph

y=(x+3)(2x-1)(2-x)

The roots are -3, 1/2, and 2

It is of the form

$$\\y=-ax^3+bx^2+cx+d\\\\

$Where a,b,c and d are real numbers and a is positive.$$$

****** I instantly know the shape of this graph. ******

Refer to this post that I did in the past to understand what I mean.

**It will help you enormously if you understand this older post !!!**

**http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed**

Here is the graph. I have hidden the y axis because it is not relevant.

you do not need a graphing calc to get this basic shape. It is easy to draw freehand.

The answer is all the x values where the graph is ABOVE the x axis. It is that easy!

You do not need to test any points!

Solutions $$(-\infty,-3)\;\;and\;\;(0.5,2)$$

If you have any questions please ask.

If you fully understand this you will be a step in front of many others :)

Melody
Apr 16, 2015

#1**+10 **

**(x + 3)(2x - 1)(2 - x) > 0**

**Setting each factor to 0, we have the following possible solution intervals....**

**(-∞, -3), (-3, 1/2), (1/2, 2), (2, ∞ )**

**We can pick a point in each interval to see if that interval satisfies the inequality**

**Picking -5 in the first interval will make the inequality true**

**This lets us know that the other interval that will "work" occurs on (1/2, 2)**

**Then, the solutions come from (-∞, -3) and (1/2, 2)**

**See the graph here.....https://www.desmos.com/calculator/1l4dwzcpor**

** **

CPhill
Apr 15, 2015

#2**+10 **

Best Answer

I would consider the graph

y=(x+3)(2x-1)(2-x)

The roots are -3, 1/2, and 2

It is of the form

$$\\y=-ax^3+bx^2+cx+d\\\\

$Where a,b,c and d are real numbers and a is positive.$$$

****** I instantly know the shape of this graph. ******

Refer to this post that I did in the past to understand what I mean.

**It will help you enormously if you understand this older post !!!**

**http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed**

Here is the graph. I have hidden the y axis because it is not relevant.

you do not need a graphing calc to get this basic shape. It is easy to draw freehand.

The answer is all the x values where the graph is ABOVE the x axis. It is that easy!

You do not need to test any points!

Solutions $$(-\infty,-3)\;\;and\;\;(0.5,2)$$

If you have any questions please ask.

If you fully understand this you will be a step in front of many others :)

Melody
Apr 16, 2015