The vertex of g(x) is (3 , 7)
Explanation:
g(x) = f(x - 2) that means g(x) is the image of f(x) after translation 2 units
to the right, so to find the vertex of g(x) let us do that:
1. Find the vertex of f(x)
2. Translate this vertex to right 2 units by adding the x-coordinate of the
vertex of f(x) by 2
3. Write the new point as a vertex of g(x)
→ f(x) = x² - 2x + 8
Assume that the vertex of f(x) is point (h , k)
→ h = [tex]\frac{-b}{2a}[/tex], where a is the coefficient of x² and b is
the coefficient of x
→ k = f(h)
→ a = 1 and b = -2
Substitute these values in the rule of h
→ h = [tex]\frac{-(-2)}{2(1)}=1[/tex]
Now find k by substitute x by h
→ k = f(1)
→ k = (1)² - 2(1) + 8 = 1 - 2 + 8 = 7
→ k = 7
The vertex of f(x) is (1 , 7)
Add the x-coordinate of the vertex of f(x) by 2
→ (1 + 2 , 7) = (3 , 7)
The vertex of g(x) is (3 , 7)
Learn more:
You can learn more about the vertex of a function in brainly.com/question/9390381
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