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4. F-BF.2.3
The vertex of the parabola represented by
f(x) = x2 - 4x + 3 has coordinates (2, -1).
Find the coordinates of the vertex of the
parabola defined by g(x) = f(x - 2).
Explain how you arrived at your answer.

Respuesta :

evgeniylevi

Answer:

(4;-1).

Step-by-step explanation:

1) to write new equation:

f(x-2)=(x-2)²-4(x-2)+3; ⇒ f(x-2)=x²-8x+15;

2) to define the new vertex:

(4; -1).

PS. the suggested way is not the shortest one; it's just to move the vertex to the right direction on 2 units.

semsee45

Answer:

Vertex of g(x) is (4, -1)

Step-by-step explanation:

Method 1

Using translations rules:

[tex]\textsf{when }\:a > 0: \quad f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]\textsf{Therefore }\quad f(x-2) \implies f(x) \: \textsf{translated}\:2\:\textsf{units right}[/tex]

If the vertex of f(x) is (2, -1)

then the vertex of g(x) is (2 + 2, -1) = (4, -1)

Method 2

Vertex form of a parabola

[tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex and a is some constant)

Given function:  [tex]f(x)=x^2-4x+3[/tex]

If the vertex of f(x) is (2, -1), then f(x) written in vertex form is:

[tex]f(x)=(x-2)^2-1[/tex]

[tex]\begin{aligned} \textsf{If}\quad g(x) & =f(x-2)\\\implies g(x) &=((x-2)-2)^2-1\\&=(x-4)^2-1\end{aligned}[/tex]

Therefore, the vertex of g(x) is (4, -1)

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