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2 years ago

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?

Mathematics

2 answers:

zhannawk [14.2K]2 years ago

6 0

Answer:

f(x) shift right 2 and up 3 to get g(x)

A is correct.

Step-by-step explanation:

Given: $f(x)=x^2$ and $g(x)=(x-2)^2+3$

We need to find transformation that occurs from f(x) to g(x).

Parent function is quadratic equation.

Concept of transformation:-

For horizontal shift:

If x changes to x+a then left or right shift.

a>0 then shift left

a<0 then shift right

For vertical shift:

If y changes to y+a then up or down shift

If b>0 then shift up by a unit

If b<0 then shift down by a unit.

$f(x)\rightarrow g(x)$

$x^2\rightarrow(x-2)^2$

Thus, f(x) shift 2 unit right.

$(x-2)^2\rightarrow (x-2)^2+3$

Thus, f(x) shift 3 unit up.

Hence, f(x) shift right 2 and up 3 to get g(x)

Andrei [34K]2 years ago

5 0

Answer:

A. right 2, up 3

Step-by-step explanation:

We have that,

The function $f(x) = x^2$ is transformed to $g(x) =(x- 2)^2+3$ .

We see that,

The function f(x) is translated 2 units to the right and 3 units upwards to obtain the function g(x).

So, the correct transformation is 'right 2, up 3'.

Hence, option A is correct.

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You put $1200 in an account that earns 3% simple interest. Y= a (1 + r)t Find the total amount in the account after four years.

olchik [2.2K]

Hello!

To find how much money total will be in the account after four years, you need to use the function, $y = a(1 + r)^{t}$ , as seen above. In this function, a is the starting value, r is the interest rate, and t is the amount of time (in years).

Before substituting values into the function, we need to convert 3% into a decimal. Remember that all percentages are out of 100, so we divide 3 by 100 and remove the percentage sign, or move the decimal two places to the left.

3/100 = 0.03 | 0.03 is the interest rate.

With all the necessary values, we can find the total amount in the account. In this case, a = 1200, r = 0.03, and t = 4.

$y = 1200(1 + 0.03)^{4}$

$y = 1200(1.03)^{4}$

$y = 1200(1.12550881)$

y = 1350.610572, which can be rounded to 1350.61 dollars.

Therefore, after 4 years, the total amount in the account will be about 1350.61 dollars.

6 0

1 year ago

Given a rectangular pyramid and a rectangular prism that have the same base and same height, how do their volumes compare? If th

Luden [163]

We know that
volume of a rectangular prism =B*h------> equation 1
where
B is the area of the base
h is the height

volume of a rectangular pyramid=(1/3)*B*h-----> equation 2
where
B is the area of the base
h is the height

substitute equation 1 in equation 2
volume of a rectangular pyramid=(1/3)*volume of a rectangular prism

the answer part a) is
volume of a rectangular pyramid=(1/3)*volume of a rectangular prism

Part b) If the pyramid was full of water, how much of the prism would it fill up?

the answer part b) is
If the pyramid was filled with water, the prism would only fill 1/3 of its volume

Part c) Name another pair of three-dimensional objects that have a relationship similar to this

cones and cylinders

volume of a cylinder =B*h------> equation 1
where
B is the area of the base
h is the height 

volume of a cone=(1/3)*B*h-----> equation 2
where
B is the area of the base
h is the height

substitute equation 1 in equation 2
volume of a cone=(1/3)*volume of a cylinder

4 0

2 years ago

Weekly demand for a particular item averages 30 units, with a standard deviation of 4. This item is managed with a fixed-order-i

aivan3 [116]

Answer:

(B)93

Explanation:

Since we are using a fixed-order-interval model,

The Amount to Order=Expected Demand During protection Interval+Safety Stock-Amount at Hand

$=d(OI+LT)+z\sigma_{d}\sqrt{OI+LT}-A$

Where:

d=weekly demand

OI=Order Interval

LT=Lead Time

z=Standard Deviation of Desired Service Level

$\sigma_{d}$ =Standard Deviation of weekly Demand

A= Amount at Hand

$=d(OI+LT)+z\sigma_{d}\sqrt{OI+LT}-A$

$[30(3 + 1)] + [1.964*4*\sqrt{3 + 1} - 43$

$= 120 + 15.712 - 43 = 92.7$

4 0

1 year ago

Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amoun

Inessa [10]

Answer:

49 square meters represent area of the square garden

Step-by-step explanation:

Each side length=7 meters

He multiplied 7 × 7 times to find the amount of space

=49 square meters

Jack is trying to measure the area of his square garden

Area of the square garden = length^2

=Length × length

Recall,

Length=7 meters

Area of the square garden= 7 meters × 7 meters

=49 square meters

5 0

2 years ago

max is bisecting a segment. first. he places the compass on one endpoint and opens it to a width larger than half of the segment

spin [16.1K]

Answer:

Keep the compass the same width and place it on the other endpoint.

Step-by-step explanation:

Max is bisecting a segment. First, he places the compass on one endpoint and opens it to a width larger than half of the segment. Then he swings an arc on either side of the segment.

Next Max's step should be: keep the compass the same width and place it on the other endpoint.

He will draw the second arc of the same radius as the first one.

Two drawn arcs intersect at two points, Max will connect these points and get the segment which bisects the given one.

7 0

2 years ago

Read 2 more answers