Question

PLEASE HELP ASAP!!!

Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 + 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?

A.Left by 4 units
B. Right by 4 units
C.Left by 8 units
D. Right by 8 units

Answer 1

A. Left by 4 units

Explanation:

ƒ(x) = x²

It has a vertex at (0, 0), and the y-axis is the axis of symmetry

g(x) = x² + 8x + 16 = (x + 4)²

You have added 4 to the value of x, so you have shifted the graph four units to the left.

Thus, to make the graphs of ƒ(x) and g(x) coincide, you should shift ƒ(x) left by 4 units.

The diagram below shows ƒ(x) in red and g(x) in green.