CPhill

-3x^2 + 2x  -  3   =  0

a  = -3     b   = 2      c   =  -3

Using the Quadratic Formula

x  = [  - b ±√ [ b^2 - 4ac]  ] /  [ 2a]  =

[ -2 ±√ [ 2^2 - 4(-3)(-3) ] ] / [ 2 * -3 ]  =

[ -2 ±√ [ 4 - 36] ] / [ -6]  =

[ -2 ±√-32 ] / [ -6]  =

[-2 ±√ [ (-1)(16)(2) ] ] / -6

[-2 ±4i√2 ] / -6  =

[ -1 ± 2i√2 ] / -3  =

[ 1 ±2i√2 ] / 3   ⇒   "B"

For the second one the distance  is  √[23^2  - 12^2 ]  = √385  =  19.6 ft   ...correct  !!!

Domain and range are correct  !!!!

Relative max occurs at ≈  (2.816, 1.089)

Relative min occurs at ≈ (1.184, - 1.089)

You have the end behavior almost correct, RP

As the function approaches + inf....the end behavior  is  - inf

As it approaches -inf.....the end behavior  is  + inf

Increasing intervals  [ where the function rises from left to right  ]  = (1.184, 2.816 )

Decreasing intervals [ where it  falls from left to right ] = (-inf, 1.184) U (2.816, inf )

Here's the graph :  https://www.desmos.com/calculator/mk1cbfvwvh

Is this all clear to you  ????

Correct !!!....positive inf on the left end......negative inf on the right end

Let's just look at this, RP : https://www.desmos.com/calculator/cb1kkobkfe

Can you answer this, now  ???

x^2 + 36  = 0  subtract 36 from both sides

x^2  = -36       take both roots

x  = ±√ - 36  = ±√ [ (-1)(36) ]  = ± i * 6  =  ± 6i

[ Remember that   √ (-1)  =  i  ]

First one

a) End behavior -  negative infinity at the left end, positive infinity at the right end

b) Neither - it is not even because it is not symmetric to the y axis....to be odd....we could "flip" the fuction on either side of the y axis and it would have to mirror the other side...this is not true for this function

c) The lead coefficient is positive

Second one

a) End behavior  - negative infinity at both ends

b) Neither   -  not symmetric to the y axis

c) The lead coefficient is negative

If we center a circle with a radius of 1 at "A"...the area of the circle  sector contained by the triangle will be :

 pi * (1)^2  (60 / 360)  =    pi/ 6  ....   (1)

And the area of the triangle is   (1/2)(3)^2 sqrt (3)/2   =  9sqrt(3)/4   .....(2)

So.....the  probability is  (1) / (2)   =  [  pi/6 ]  / [ 9 sqrt (3) / 4 ]   ≈  13.44%

Here's the first one....if we consider the points to be A, B ,C, D...etc, we can choose any two of the points without regard to  order.....this will result in   C(9,2)   ⇒   36  segments being drawn

16

(a + b)(3a - b) (2a + 7b)      expand the first two factors
 

( 3a *a + 3ab - ab - b^2) (2a  + 7b) =     simplify the terms in the left parentheses

(3a^2 + 2ab - b^2)(2a + 7b)  =    expand the first terms over the second

3a^2 * 2a  +  2ab * 2a -  b^2* 2a   + 3a^2* 7b +  2ab*7b - b^2*7b   =

6a^3 + 4a^2b - 2ab^2 + 21a^2b + 14ab^2 - 7b^3   =

6a^3 + 25a^2b + 12ab^2 - 7b^3