Here are some points for all who are working hard and over coming challenges and helping <3 ( p.s there is another one in adv
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Given:
The two functions are:
To find:
The type of transformation from f(x) to g(x) in the problem above and including its distance moved.
Solution:
The transformation is defined as
.... (i)
Where, a is horizontal shift and b is vertical shift.
- If a>0, then the graph shifts a units left.
- If a<0, then the graph shifts a units right.
- If b>0, then the graph shifts b units up.
- If b<0, then the graph shifts b units down.
We have,
The function g(x) can be written as
...(ii)
On comparing (i) and (ii), we get
Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).
Answer:
<em>Vertex: (3,4)</em>
Step-by-step explanation:
<u>Vertex form of the quadratic equation</u>
The vertex form of the quadratic function has the following equation:
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
The parabola is given as:
Comparing with the equation:
a=2, Vertex: (3,4)
The graph of the parabola is shown in the image below
