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The graphs of f(x) and g(x) are shown below:


graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 5, 0


If f(x) = (x + 7)2, which of the following is g(x) based on the translation? (5 points)



g(x) = (x + 9)2

g(x) = (x + 5)2

g(x) = (x − 9)2

g(x) = (x − 5)2

Verified Answer :

nobillionaireNobley

Quadatic equation written in vertex form is of the form \(a(x-h) ^{2} +k\), where (h, k) is the vetex of the graph.

Here, h = -5 and k = 0
putting thhese into the equation, we have,
 \(a(x-(-5)) ^{2} +0=a(x+5) ^{2}\)
Therefore, \(g(x)=(x+5) ^{2}\)

g(x) based on the translation is g(x) = (x + 5)² which is correct option (D).

What is graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Shifting of a graph is done by adding any arbitrary constant to the function in shifting.

Given that graph of function f of x open upward and has its vertex at negative 7, 0.

Graph of function g of x opens upward and has its vertex at negative 5, 0

Vertex form of a quadratic equation has the following formula: where (h, k) is the graph's vetex.

f(x) =  (x + 7)²

Then simply plug-in the values of h and k which are h = -5 and k = 0

g(x) = (x + 5)²,

Hence, this is g(x) based on the translation.

Learn more about graph here:

https://brainly.com/question/16608196

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