Answer:
#1
The term -2 vertically stretches the graph and reflects it across the y axis
The term -1 shifts the graph down by 1 unit.
#2
The quadratic regression equation is y = 2.61x^2 - 115.27x + 1568.06 (rounded to 2 decimal places)
#3
Plug in the values
2.61(23)^2 - 115.27(23) + 1568.06 = y
2.61(529) - 115.27(23) + 1568.06 = y
1,380.69 - 2,651.21 + 1568.06 = y
297.54 = y
(note I showed work here and not in the step by step because the answer asked for work to be shown)
Also just for you to know the equation obtained in #2 is gotten just by plugging the table into desmos with desmos solving for the best fit quadratic regression equation. Just google desmos quadratic regression and it should come up with a graph set up for this.
Please ask if you have any questions.
EDIT for new answers
2.12
g(-2) = -2
g(0) = 0
g(2) = 2
g(4) = -3
g(6) = -3
Explanation: The piecewise basically says anything less than or equal to two is itself, anything greater is equal to -3.
2.13
So the top number, 15 is the maximum value for y and the most growth occurs at the halfway point of y so we plug in 15/2 for y and solve for x.
15/2 = 15/(1+4e^-0.2x) then we can multiply both sides by its reciprocal and get the same denominators which we can then remove to get
2 = 1 + 4e^-0.2x subtract 1 divide by 4
1/4 = e^-0.2x then ln both sides
ln(1/4) = ln(e^-0.2x) the -0.2x can be moved out front
ln(1/4) = -0.2xln(e)
ln(1/4) = -0.2x(1)
ln(1/4) = -0.2x
ln(1/4)/(-0.2) = x
x = 6.93
then y is 15/2 = 7.5
So our point is (6.93, 7.5)
