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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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Step-by-step explanation:

(3 1/3)(5 1/4) =

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1 year ago

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. A cyclist pedals his bike 6.5 km up a mountain road, which has a steady incline. By the time he has reached the top of the mou

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Answer:

9.72°

Step-by-step explanation:

Step one

Given data

let the hypotenuse be the distance the cyclist traveled = 6.5km

and let the opposite be the height of the mountain = 1.1 km

Step two:

Applying SOH CAH TOA

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1 year ago

In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is . The area of polygon ABCDE is s

Gekata [30.6K]

Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

$P=2b+2h$

In this problem

$b=ED=2\ units$

$h=AE=6\ units$

substitute

$P=2*2+2*6=16\ units$

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

$P=BD+DC+BC$

In this problem we have

$BD=AE=6\ units$

$DC=BC$

Applying the Pythagoras theorem

$DC^{2}=4^{2}+3^{2}$

$DC^{2}=25$

$DC=5\ units$

substitute

$P=6+5+5=16\ units$

Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

$P=16\ units$

the perimeter of the triangle is

$P=16\ units$

the ratio is equal to

$\frac{16}{16} =1$

therefore

the answer Part 1) is the option B

$1$

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

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Area of the triangle is equal to

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