Answer:
The following are the answer to this question:
Step-by-step explanation:
In the given question the numeric value is missing which is defined in the attached file please fine it.
Calculating the probability of the distribution for x:
The formula for calculating the mean value:
use formula for calculating the Variance:
calculating the value of standard deivation:
Standard Deivation (SD) =
Answer:
1. f₁(x)=-x²+2x-2
2. f₂(x)=-x²+6x-10
3. f₃(x)=-x²-2
4. f₄(x)=-x²+10x-26
5. f₅(x)=-x²-2x-2
6. f₆(x)=-x²
Step-by-step explanation:
1. we have that f(x) is translated right by 1 unit , also
according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2
2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)
y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10
3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)
y+2 = -(x)² ⇒ y=-x²-2
4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)
y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26
5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)
y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2
6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)
y+0 = -(x+0)² ⇒ y=-x²
