How to graph f(x)=(x-2)^2+3
1 answer:
Using translation concepts, the graph of f(x) = (x - 2)² + 3 is given at the end of the question.
<h3>What is a translation?</h3>A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that the parent and the translated function are given, respectively, by:
- g(x) = x².
- f(x) = (x - 2)² + 3.
The translations are as follows:
- Right two units, as x -> x - 2.
- Up 3 units, because f(x) = g(x) + 3.
Hence the graphs are given at the end of the answer, with the parent function in red and the translated function f(x) = (x - 2)² + 3 in green.
More can be learned about translation concepts at brainly.com/question/4521517
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For this case, the first thing we must do is define variables:
p: plane speed
w: wind speed
With the wind in favor, the speed is:
With the wind against the speed is:
Rewriting both equations, we have the following system of equations:
Then, solving the system of equations (graphically for example), we have the solution is:
Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h
p: plane speed
w: wind speed
With the wind in favor, the speed is:
With the wind against the speed is:
Rewriting both equations, we have the following system of equations:
Then, solving the system of equations (graphically for example), we have the solution is:
Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h