Question

F(x)+x^2+3x+2 is shifted 2 units left. the result is g(x). what is g(x)?

Answer 1

Adding 2 to all the x's shifts the function left.

g(x) = (x+2)² + 3(x+2) + 2

simplify it a bit ...

g(x) = (x+2)² + 3x + 6 + 2

g(x) = (x+2)² + 3x + 8

g(x) = x² + 4x + 4 + 3x + 8

g(x) = x² + 7x +12

Answer 2

g(x) = x² + 7x + 12

Explanation:

f(x) = x² + 3x + 2 is shifted 2 units left.

We have to find new function formed g(x)

Shifting of 2 units left means

g(x) = [x-(-2)]² + 3[x-(-2)] +2

= (x+2)² + 3 (x+2) + 2

= x² + 4x + 4 + 3x + 6 + 2

= (x² + 7x + 12)

Therefore, the new function will be g(x) = x² + 7x + 12