Question

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

Answer 1

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 +2

• f(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 - 23

• So 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.

Answer:

             So the correct option is right 5, down 23