Answer:
look below
Step-by-step explanation:
y = 2 (x + 3)^2 - 2
Geometric figure: parabola
Alternate forms:
y = 2 (x + 2) (x + 4)
y = 2 (x^2 + 6 x + 8)
-2 x^2 - 12 x + y - 16 = 0
Expanded form:
y = 2 x^2 + 12 x + 16
Roots:
x = -4
x = -2
<u>Properties as a real function:
</u>
Domain
- R (all real numbers)
Range
- {y element R : y>=-2}
Partial derivatives:
d/dx(2 (x + 3)^2 - 2) = 4 (x + 3)
d/dy(2 (x + 3)^2 - 2) = 0
Implicit derivatives:
(dx(y))/(dy) = 1/(12 + 4 x)
(dy(x))/(dx) = 4 (3 + x)
Global minimum:
min{2 (x + 3)^2 - 2} = -2 at x = -3
Answer:
a = 15
Step-by-step explanation:
This is your given:
You are going to want to get a alone to get what a equals.
Multiply 3 on both sides to get the a alone
Let's start with the x coordinates.
-8 is on the left, and -4 to the right, so that will help organize this.
the line goes from -8,-9 to -4,-8. it moved 4 over the x axis and rose 1 over the y axis.
rise/run so 1/4 is the slope.
y=(1/4)x - 7
First you have to simplify the equation. 7m+5m-5 = -5+12m
Then you can add like terms.
12m-5 = -5+12m
Add 5 to both sides
12m = 0+12m
Subtract 12 to both sides
0=0
This equation has infinite solutions
Answer:
C
Step-by-step explanation:
For the first one, there is a ratio of change greater than one so that is exponential growth.
The second one has exponential decay but its x is negative making it actually exponential decay even if graphed.
The third one has positive growth over an interval of negative x, so in terms of x there is exponential decay.
The fourth one is neither and if graphed is just points as there is a specific solution set.
In conclusion, the third is exponential decay!
Hope this helps :)
