Four less than the product of twice a number and eight

Always remember general rules of transformation.

1) Vertical Shift:

y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.

2) Horizontal Shift:

y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.

3) Reflection across x-axis

y= - f(x) ; reflect the graph of f across the x-axis.

Now,

The parent function is y= -(x+2)²

1. y= -(x+4)²

In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²

So, according to rule 2 it will shift the parent function to the left by 2 units.

E is the correct option.

2. y = - (x + 2)² - 2

In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2

So, according to rule 1, it will shift the graph down by 2 units.

F is the correct option.

3. y=(x - 2)²

In this question, two operations are performed on the parent function.

First one, -4 is added with x+2 so we get x+2-4= x-2

Second one, -1 is multiplied with parent function.

By performing the two operations at a time we get a new function which is

y=-(-(x+2-4)²)=(x-2)²

The first operation will translate the parent function 4 units right (according to rule 2).

The second operation will reflect the graph across x-axis(according to rule 3).

D and translation 4 units to right is correct option.

4. y= 2 -(x+2)²

In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.

C is the correct option.

5. y= -x²

In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²

So, according to rule 2 it will shift the graph right by 2 units.

B is the correct option.

6. y= (x+2)²

In this question, -1 is multiplied with parent function and we get

y= -(-(x+2)²)= (x+2)²

So, according to rule 3 , graph is reflected across x-axis.

D is the correct answer.

The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).

The area that will be painted blue is 69.97 square feet.

How to find the area that will be painted blue?

Remember that for a rectangle of length L and width W, the surface area is given by:

In this case we have:

• L = (8 + 2/5)ft
• W = (16 + 2/3) ft.

Replacing that in the area equation:

And we know that half the wall is painted, so the area that will be blue is:

If you want to learn more about areas:

brainly.com/question/24487155

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