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.