"The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?

Answers

Answer 1

Answer: G(x)=x²
The graph has moved to the right 4 units, therefore the new graph will be:
H(x)=(x-4)²

It has also move 4 units up, therefore the new graph will be:
F(x)=(x-4)²+4

Answer:
F(x)=(x-4)²+4

Answer 2

Answer:

y = (x - 4)² + 4

or y = x² - 8x + 20

Further explanation

Transformation of a graph is changing the shape and location of a graph.

There are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).

In this case, the transformation is shifting horizontally or vertically.
Translation (or shifting): moving a graph on an analytic plane without changing its shape.
Vertical shift: moving a graph upwards or downwards without changing its shape.
Horizontal shift: moving a graph to the left or right downwards without changing its shape.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:

$\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.
$\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.

That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:

$\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.
$\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Hence, the combination of vertical and horizontal shifts is as follows:

$\boxed{\boxed{ \ y = f(x \pm h) \pm v \ }}$

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right

Given: $\boxed{ \ g(x) = x^2 \ becomes \ f(x) = ? \ }$

In the graph, notice the shifting of the vertex from (0, 0) to (4, 4).

From this, we can describe that from g(x) to f(x) there has been a shift to the right 4 units and upward 4 units.

Let us construct f(x) from g(x).

$\boxed{ \ g(x) = y = x^2 \ } \rightarrow \boxed{ \ f(x) = y = (x + h)^2 + v \ }$

We set h = -4 and v = +4 and we get the equation f(x) as

$\boxed{\boxed{ \ f(x) = (x - 4)^2 + 4 \ }}$

Let's expand it if we want to represent a standard form of a quadratic function, like this:

$\boxed{ \ f(x) = x^2 - 8x + 16 + 4 \ }$

$\boxed{\boxed{ \ f(x) = x^2 - 8x + 20 \ }}$

Conclusion

The graph of f(x) is drawn by the combination of shifting the graph of g(x) to the right 4 units and upward 4 units.

Learn more

Transformations that change the graph of (f)x to the graph of g(x) brainly.com/question/2415963
The similar problem brainly.com/question/1369568
Determine the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: transformations, the graph of f(x), resembles, g(x) = x², f(x) = (x - 4)² + 4, y = x² - 8x + 20, translation, shifting, right, upward, horizontal, vertical

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Use the information to answer the question.A store is having a sale on hats. The sale is buy one hat get one 50% off. The original price of one hat is $24.98. Alex bought several hats, and the
total cost was $187.35.

Answers

Answer:

10 hats

Step-by-step explanation:

Original price

$24.98

Sale price

$24.98*1.5 = $37.47 for two hats

Total cost

$187.35

Hats sold:

187.35/37.47 *2 = 10 hats

Sue buys 5 pieces of fabric.Each piece is 1 7/10 yards long.What is the total length of the fabric she buys?One yard of the fabric costs $5.How much does she pay for all 5 pieces of fabric?

Answers

Answer:

1. 8.5 yards.

2. $42.5

Step-by-step explanation:

We have been given that Sue buys 5 pieces of fabric. Each piece is $1(7)/(10)$ yards long.

1. To find the total length of fabric bought by Sue we will multiply length of each fabric piece by 5.

$\text{Total length of the fabric}=5* 1(7)/(10)\text{ yards}$

$\text{Total length of the fabric}=5* (17)/(10)\text{ yards}$

$\text{Total length of the fabric}=(17)/(2)\text{ yards}$

$\text{Total length of the fabric}=8.5\text{ yards}$

Therefore, Sue bought 8.5 yards of fabric.

2. 1 yard of fabric costs $5.

So 8.5 yards of fabric will cost : 5*8.5

$\text{Total cost of the fabric}=5* 8.5$

$\text{Total cost of the fabric}=42.5$

Therefore, the cost of total fabric bought by Sue is $42.5.

Convert to metric 7gram = mg

Answers

Answer:

I think it's 7000 mg because 1 gram equals to 1000 milligrams and so well if 1 gram equals to 1000 so 7 gram would be more and we have to multiply 1000 by 7 which give us 7000

Answer:

7000 mg

Step-by-step explanation:

to convert grams into milligrams you have to multiply by 1000, 7 times 1000 is 7000

What is the vertex of the quadratic function f(x) = (x-2)(x-2)