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Which function could be represented by the graph on the coordinate plane?

f(x) = (x – 8)2 + 6
f(x) = (x + 8)2 + 6
f(x) = (x + 8)2 – 6
f(x) = (x – 8)2 – 6
(I know it isn't the second option)

Which function could be represented by the graph on the coordinate plane fx x 82 6 fx x 82 6 fx x 82 6 fx x 82 6I know it isnt the second option class=

Respuesta :

kudzordzifrancis

Answer:

[tex]f(x)=(x-8)^2-6[/tex]

Step-by-step explanation:

The given graph was obtained after a transformation of the parent function [tex]y=x^2[/tex].


The equation of the transformed function will now be in the form,


[tex]f(x)=a(x-h)^2+k[/tex], where [tex](h,k)[/tex] is the vertex of the graph.


Since the vertex of the graph is now in the fourth quadrant, the coordinate will be in the form [tex](x,-y)[/tex].

Based on the options given we can conclude that the vertex has coordinates [tex](8,-6)[/tex] and [tex]a=1[/tex].


If we substitute these values in to the equation, we obtain, [tex]f(x)=1(x-8)^2+-6[/tex].


This simplifies to,

[tex]f(x)=(x-8)^2-6[/tex].


Hence the correct answer is D

Transformation of a function is shifting the function from its original place in the graph.

Function which represents the graph on the coordinate plane is,

[tex]y=(x-8)^2-6[/tex]

Hence the option 4 is the correct option.

What is transformation of a function?

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

  • Horizontal shift- Let the parent function is [tex]f(x)[/tex].Thus by replacing parent function with [tex]f(x-b)[/tex] shifts the graph b units right and by replacing parent function with [tex]f(x+b)[/tex]shifts the graph b units left.
  • Vertical shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x)-c[/tex] shifts the graph c units down and by replacing parent function with [tex]f(x)+c[/tex] shifts the graph c units up.

Given information-

In the given problem the parabola is shown which shifted horizontally and vertically from the origin.

The vertex form of the parabola can be given as,

[tex]y=a(x-h)^2+k[/tex]

Here, [tex](h,k)[/tex] is the vertex of the equation.

As the graph is shifted right horizontally with some unit (8) from the option and shifted down vertically with some unit (6) from the option. Thus the equation can be written as,

[tex]y=(x-8)^2+(-6)\\y=(x-8)^2-6[/tex]

Hence function which represents the graph on the coordinate plane is,

[tex]y=(x-8)^2-6[/tex]

Hence the option 4 is the correct option.

Learn more about the transformation of a function here;

https://brainly.com/question/10904859

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