Question

Which translation maps the graph of the function f(x) equals X to add to the function GX equals X2 onto the function g(x) = x2 + 2x +6

Answer 1

Answer:

left 1 unit, up 5 units

Step-by-step explanation:

To answer the question:

Which translation maps the graph of the function f(x) = x² onto the function g(x) = x² + 2x + 6?

we need to find the vertex of g(x), as follows:

• x-coordinate of the vertex (h): -b/(2a) = -2/(2*1) = -1

• y-coordinate of the vertex (k): y = (-1)² + 2(-1) + 6 = 5

Therefore, g(x) can be rewritten as:

g(x) = a(x - h)² + k

g(x) = (x + 1)² + 5

which is the equation of f(x) = x² translated 1 unit to the left and 5 units up.