Mathematics, 02.12.2019 03:31 SirMLGLemons

Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?

a.4 units to the left

b.4 units to the right

c.8 units to the left

d.8 units to the right

Answers: 1

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Answers

Answer from: Mercedes12152002

4 units to the left.

Further explanation

Given:

Before translation: y = 2(x – 15)² + 3After translation: y = 2(x – 11)² + 3

Question:

Which phrase best describes the translation?

The Process:

In general, given the graph of $\boxed{y = f(x)}$ and $\boxed{ \ k 0 \ }$ , we obtain the graph of

$\boxed{y = f(x + k)}$ by translating the graph of $\boxed{y = f(x)}$ to the left k units.

$\boxed{y = f(x - k)}$ by translating the graph of $\boxed{y = f(x)}$ to the right k units.

Before translation: y = 2(x – 15)² + 3After translation: y = 2(x – 11)² + 3

Find out the changes in the brackets between the before and the after.

$\boxed{ \ (x - 15) + k = (x - 11) \ }$

$\boxed{ \ - 15) + k = - 11 \ }$

$\boxed{ \ k = 15 - 11 \ }$

$\boxed{ \ k = 4 \ }$

Let's look again.

Before translation: y = 2(x – 15)² + 3

$\boxed{ \ 4 \ units \ to \ the \ left \ }$

After translation: y = 2[(x – 15) + 4]² + 3

After translation: y = 2(x – 11)² + 3

This has been proven.

Notes:

Given k ∈ R, after the transformation coordinates of each point, (x, y) on the graph of $\boxed{y = f(x)}$ change as follows:

Horizontal shift: $\boxed{Function: y = f(x + k)} \boxed{Coordinates: (x - k, y)}$ Vertical shift: $\boxed{Function: y = f(x) + k} \boxed{Coordinates: (x, y + k)}$ Horizontal reflection: $\boxed{Function: y = f(-x)} \boxed{Coordinates: (-x, k, y)}$ Vertical reflection: $\boxed{Function: y = -f(x)} \boxed{Coordinates: (x, -y)}$ Horizontal stretch and shrink: $\boxed{Function: y = f(kx)} \boxed{Coordinates: (\frac{1}{k}(x), y)}$ Vertical stretch and shrink: $\boxed{Function: y = kf(x)} \boxed{Coordinates: (x, ky)}$ Learn moreWhat transformations change the graph of (f)x to the graph of g(x)? A triangle is rotated 90° about the origin Determine the coordinates of a point after the triangle is rotated 270° about the origin

Keywords: which phrase best describes the translation, from the graph y = 2(x – 15)² + 3, to the graph of y = 2(x – 11)² + 3, transformation, 4 units to the left, to the right

Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(

Answer from: Ostritch8336

The graph of the function $\boxed{y = 2{\left( {x - 11} \right)^2} + 3}$ can be obtain by shifting units to the left of graph $\boxed{y = 2{\left( {x - 15} \right)^2} + 3}$ .

Further explanation:

The value of $f\left( {x - c} \right)$ at is the same as the value of $f\left( x \right)$ at x - c .

Therefore to obtained the graph of $y = f\left( {x - c} \right)$ , shifts the graph of $y = f\left( x \right)$ to the left by units.

The value of $f\left( {x + c} \right)$ at is the same as the value of $f\left( x \right)$ at x + c .

Therefore to obtained the graph of $y = f\left( {x + c} \right)$ , shifts the graph of $y = f\left( x \right)$ to the right by units.

Given:

Before translation the equation of the graph is $\boxed{y = 2{\left( {x - 15} \right)^2} + 3}$ .

After translation the equation of the graph is $\boxed{y = 2{\left( {x - 11} \right)^2} + 3}$ .

Calculation:

Consider the shift of the graph as units.

Now find the translation of the graphs.

$\begin{aligned}2{\left( {x - 11} \right)^2} + 3 &= 2{\left( {x - 15 + c} \right)^2} + 3 \\{\left( {x - 11} \right)^2} &= {\left( {x - 15 + c} \right)^2} \\\left( {x - 11} \right) &= \left( {x - 15 + c} \right) \\- 11& =-15 + c \\4 &= c \\ \end{aligned}$

Hence, the graph of the function $\boxed{y = 2{\left( {x - 11} \right)^2} + 3}$ can be obtain by shifting 4 units to the left of graph $\boxed{y = 2{\left( {x - 15} \right)^2} + 3}$ .

kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the function

2. Learn more about equation of circle

3. Learn more about range and domain of the function

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Conic section

Keywords: translation, equation, parabola, shift left, shift right, horizontal, vertical, before translation, after translation.

Answer from: Quest

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn

Answer from: Quest

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.

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