Answer
The resultant function is
f(x) = 2x² + 6x + 13
Step-by-step explanation
When a function g(x) is translated horizontally along the x-axis by a units, the new function is represented as
g(x + a) when the translation is by a units to the left.
g(x - a) when the translation is by a units to the right.
When a function g(x) is translated vertically along the y-axis by b units, the new function is represented as
g(x) + b when the translation is by b units upwards.
g(x) - b when the translation is by b units downwards.
So, for this question, where the function g(x) = x² is translated 3 units up and 4 units left. The new function is
g(x)' = g(x + 3) + 4 = (x + 3)² + 4
The function is now stretched by a factor of 2.
Stretching a function by a factor simply multiplies that function by the factor. So, our function becomes
f(x) = g(x)' = 2 [(x + 3)² + 4]
=
Hope this Helps!!!