# Math Help - sketch cubic

1. ## sketch cubic

1.) Sketch the graph of function y=4x^3 - 8x^2-11x-3
I tried it, and got (x-3)(4x^2+4x+1) I can't factorise the quadratic to solve, need help

2.) (3w/2 - 5/4w)^3
Im clueless with this one i tried making the same common denominator, didnt help one bit, please provide explanation and full answers please.

2. Originally Posted by andrew2322

1.) Sketch the graph of function y=4x^3 - 8x^2-11x-3
I tried it, and got (x-3)(4x^2+4x+1) I can't factorise the quadratic to solve, need help
If you can't factorise, you can always solve it using the quadratic equation. However, in this case, it can be factorised: $(x-3)(4x^2+4x+1) \;\Rightarrow (x-3)(2x+1)^2$

2.) (3w/2 - 5/4w)^3
Im clueless with this one i tried making the same common denominator, didnt help one bit, please provide explanation and full answers please
$\left(\frac{3w}{2} - \frac{5}{4w}\right)^3$
= $\left(\frac{6w^2-5}{4w}\right)^3$
= $\frac{1}{64w^3} (6w^2-5)^3$ = 0 for x intercepts.
But $\frac{1}{64w^3} \not = 0 \Rightarrow w = 0$ is an asyptote
Therefore $(6w^2-5)^3 = 0$
$6w^2-5 = 0$
$w = \pm\sqrt{\frac{5}{6}}$

Now that you know the x intercepts, plot a few points, and find the limits.

3. Hello, Andrew!

1) Sketch the graph of: . $y \:=\:4x^3 - 8x^2-11x-3$

I tried it and got: . $(x-3)(4x^2+4x+1)$ . . . . Good!
I can't factorise the quadratic. . . . . you can't?
The function is a "positive cubic"
. . It rises to the right and falls to the left.

It factors to: . $y \:=\:(x-3)(2x+1)^2$

The x-intercepts are: . $3\text{ and }-\frac{1}{2}$

Since the intercept $x = -\frac{1}{2}$ has multiplicity 2,
. . the graph is tangent to the x-axis there.

Code:
              |
|         *
|
-½ |        *
- - - * + - - - * - -
*   *     * 3
*    |  *
|
*     |
|

$2)\;\;\left(\frac{3w}{2} - \frac{5}{4w}\right)^3$

Instructions?
. . Are we supposed to expand and simplify it?

4. ## Thanks

Thanks for the help, but what's an asyptote?