CPhill

y   =  -6x^2  -  1

This is a parabola  that opens downward....it has no minimum

Notice  that  y  will be a maximum when  x  = 0

So.....the  max occurs at    (0, -1)

Here's a graph to verify this  :

https://www.desmos.com/calculator/4i2zlzorca

16.

The sum is given by

2 [  1  - (1/3)^15 ] /  [ 1  - 1/3 ]   =   3   {rounded }  

17.  The total distance is given by

20 [ 1 - (2/5)^(n )]  /[ 3/5 ] -10   where n  is the nth bounce

So ....for the 5th bounce we have

t10 + 20 [ 1 - (2/5)^(5)] [ 3/5 ] =  22 + 124 / 125   ft

14.

The first term is  3(1)  - 4  =   -1    and the last is  3(18) - 4  = 50

So....the sum is

[ -1 + 50 ] (18/2)  =  49 * 9   =  441 

15.  The first term is  3(1)  - 3  =   0     and the last is  3(10) - 3  =  27

So  the sum is  [ 0 + 27 ] * (10/ 2)  =  27 * 5   =  135

12.

There are 15 terms

The sum is   

(-15 + 195) * (15/2)  =  1350

13.   The second answer is correct

1.

The domain of both functions is the set of real numbers less than or equal to 0.

2.  When x  = -3.....function A  = -5     and Function B  = -2

So    g(-3)  >  f(-3)

4x + ay  = -8

2x + y  =  b

Multiply the second equatiion by 2   all the way through

4x + ay  = -8

4x + 2y  = 2b

This system will have infinite solutions  when  the   equations  are exactly the same......so....for this to happen    ⇒

a  =  2      and   b  =  -4

The letter  "m"

Function A has two x intercepts, (3,0)  and (1,0)

Function B,  y   = l x l - 2 , also has  two x intercepts  = (2,0)  and (-2, 0 )

So.....the have the same number of x intercepts......{ but not the same x intercepts }

The slope of the line is   [6 - 2 ]  /  [-2 + 6 ]  = 4 / 4  = 1

The equation of the line passing through these two points is

y  = 1 ( x + 2)  +  6

y = x  + 8 

To find the height of the triangle....find where the line intercepts the y axis....let x  = 0

y  =  0 +  8   =   8

To find the base of the triangle, let y  = 0

0  = x +  8

-8  = x         take the absolute value of this  =  8

So.....the area of the triangle is   (1/2) base * height  =  (1/2) * 8 * 8  =  

(1/2 * 64   =     

32 units^2

2x^2  - 3x  - 7  = 36      subtract 36 from both sides

2x^2  - 3x  - 43  = 0

Since the discriminant  is

(-3)^2  - (4)(2)(-43)

9  + 344

353 > 0

We wil have two real roots