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What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function

g(x) = (x + 5)2 + 3?

User Malthe
by
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2 Answers

3 votes
the +3 is the vertical and the +5 tells you horizontal. so this graph moves 3 up and 5 left. But since it only wants vertical that would be the +3
User Badcompany
by
8.1k points
6 votes

Answer:

Shifted 3 units upwards.

Explanation:

We have been given a parent function
f(x)=x^2 and a translated function
f(x)=(x+5)^2+3. We are asked to determine the vertical translation from the parent function to
f(x)=(x+5)^2+3.

Let us recall translation rules.

Horizontal translation:


f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}


f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}

Vertical translation:


f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}


f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}

Upon looking at our given function, we can see that the value of 'a' is positive 5 inside parenthesis, so our graph is shifted to left by 5 units.

We can also see that the value of 'a' outside parenthesis is positive 3, therefore, the graph of parent function is shifted upwards by 3 units to get the graph of function
f(x)=(x+5)^2+3.

User Arjun Shahi
by
8.2k points

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