Given: Two functions f(x) = x^2 and g(x) = x^2 – 10x +2
To find: Which Translation maps the vertex of the graph of the function f(x) onto the vertex of the function g(x)?
Solution:Now we have given Two functions f(x) = x^2 and g(x) = x^2 – 10x +2f(x) = x^2 is a vertical parabola which open upward with vertex at point (0,0)Now g(x) can be written as:
g(x) - 2 = x^2 – 10x
g(x) - 2 + 25 = x^2 – 10x + 25
g(x) + 23 = (x - 5)^2
g(x) = (x - 5)^2 - 23So the given function g(x) is a vertical parabola with the vertex at point (5,-23).Now from this point we can see that the translation is 5 units to right as it is positive and 23 units towards down as it is negative.
So the correct option is right 5, down 23
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