Determine the equation of g(x) that results from translating the function f(x) = x2 + 3 upward 14 units.
g(x) = (x + 17)2
g(x) = (x + 14)2 + 3
g(x) = x2 - 11
g(x) = x2 + 17
x^2+3 + 14
Does this mean the answer is D?
g(x) = (x + 17)2
g(x) = (x + 14)2 + 3
g(x) = x2 - 11
g(x) = x2 + 17
correct.
To determine the equation of g(x) that results from translating the function f(x) = x^2 + 3 upward 14 units, we need to understand how the translation affects the equation.
When a function is translated upward, it means that every y-value (output) of the function is increased by a constant value. In this case, we are translating f(x) upward by 14 units.
To achieve this translation, we add 14 to the equation of f(x). Therefore, the correct equation for g(x) would be:
g(x) = (x^2 + 3) + 14
Simplifying this equation, we obtain:
g(x) = x^2 + 17
Therefore, the correct equation for g(x) is g(x) = x^2 + 17.