function g is a transformation of the parent function f(x)=x^2 the graph of g is a translation right 5 untits and up 1 unit of the graph of f. write the equation for g in the form y=ax^2+bx+c.

Answer 1

To translate the graph of the parent function f(x) = x^2 to the right 5 units and up 1 unit, we can use the equation:

g(x) = a(x - h)^2 + k

where (h, k) represents the coordinates of the vertex of the graph. In this case, h represents the horizontal translation and k represents the vertical translation.

Since we want to translate the graph to the right 5 units, h = -5. And since we want to translate it up 1 unit, k = 1.

Substituting these values into the equation, we get:

g(x) = a(x - (-5))^2 + 1

Simplifying further:

g(x) = a(x + 5)^2 + 1

This is the equation for g in the form y = ax^2 + bx + c, where a = 1, b = 10, and c = 1.