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which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x 2? right 5, down 23 left 5, down 23 right 5, up 27 left 5, up 27

User Darelf
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2 Answers

3 votes
Vertex form of the function g(x) is:
g (x) = x² - 10 x + 2 = x² - 10 x + 25 - 25 + 2=
= ( x - 5 )² - 23
h = 5, k = - 23
Answer: A) Right 5, down 23.
User Alex Chadyuk
by
8.7k points
2 votes

Answer:


5 units to the right and
23 units down

Explanation:

we have


f(x)=x^(2)

This is a vertical parabola open upward with vertex at point
(0,0)


g(x)=x^(2) -10x+2

Step 1

Convert the function g(x) into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation


g(x)-2=x^(2) -10x

Complete the square. Remember to balance the equation by adding the same constants to each side


g(x)-2+25=x^(2) -10x+25


g(x)+23=x^(2) -10x+25

Rewrite as perfect squares


g(x)+23=(x-5)^(2)


g(x)=(x-5)^(2)-23

The function g(x) is a vertical parabola with the vertex at point
(5,-23)

Step 2

Find the rule of the translation


(0,0)-------> (5,-23)


(x,y)-------> (x+5,y-23)

That means

The translation is
5 units to the right and
23 units down

User Karimi
by
8.6k points

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