Question

The graph of the parent function p( x) = x 2 passes through the point R(13, 169). The graph of p is transformed such that the new graph represents the function f( x) = ( x + 6) 2 − 10. If this transformation translates point R to a new location R', what is the x-coordinate of R'?

Answer 1

The x-coordinate of R' is 7

Explanation:

we have

`p(x)=x^2`

This is the equation of a vertical parabola, open upward

The vertex is the point (0,0)

`f(x)=(x+6)^2-10`

This is the equation of a vertical parabola, open upward

The vertex is the point (-6,-10)

so

The transformation of

p(x) -----> f(x)

(0,0) -----> (-6,-10)

The rule of the transformation is

(x,y) -----> (x-6,y-10)

That means ----> The translation is 6 units at left and 10 units down

Applying the rule of the translation to point R

R(13, 169) ------> R'(13-6, 169-10)

R(13, 169) ------> R'(7, 159)

therefore

The x-coordinate of R' is 7