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The graph of f(x) = x2 is translated to form
g(x) = (x – 2)2 – 3.

Sagot :

A parabola opens up. It goes through (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).

What is graph?

A network can be mathematically represented as a graph, which shows the connections between the lines and the points.

Figure represents graph of  f(x) =[tex]x^{2}[/tex] and g(x) =(x-[tex]2)^{2}[/tex] —3

The X-axis shift is represented by the new function g(x) = f(x—c) and The Curve is moved c units along the right side of the X-axis in the f(x) graph.

The new Y-axis shift function is represented by g(x) = f(x) + b. The curve is moved b units along the Y-upward axis's direction in the graph of f(x).

If you look at the graphic, you can see that the vertex of f(x) has its X-axis and Y-axis displaced by 2 units and 3 units, respectively, to produce the value g(x)

Now, g(x) = (x-[tex]2)^{2}[/tex] —3  = f(x-2) + (-3)

Therefore, the new vertex we get is (2,-3)

g(0) = (0-[tex]2)^{2}[/tex] —3

g(0) = 4-3

g (0) = 1

As a result, g(x) passes through (0,1)

Learn more about on graph, here:

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