Question

Describe how the graph of $y=x^2$ can be transformed to the graph of the given equation $y=x^2-14$.

• A. Shift the graph of $y=x^2$ right $14$ units.
• B. Shift the graph of $y=x^2$ up $14$ units.
• C. Shift the graph of $y=x^2$ left $14$ units.
• D. Shift the graph of $y=x^2$ down $14$ units.

Answer 1

The correct option is D

Shift the graph of $y=x^2$ down $14$ units.

Explanation for the correct option :

The given graph is $y=x^2$ .

The transformed graph is $y=x^2-14$.

To shift a graph $y=f\left(x\right)$ downwards, subtract constant from outside of the function, i.e. $y=f\left(x\right)-c$ .

Subtracting integers from the graph equation moves the graph downwards.

Hence, option (D) is correct.

Explanation for the incorrect options : (Option A)

To shift a graph right, subtract inside from the function's argument.

For a function $y=f\left(x\right)$ ,subtract $c$ units from inside the function's argument i.e. $y=f(x-c)$ .

Therefore, option $\left(A\right)$ is incorrect.

Option (B)

To shift a graph $y=f\left(x\right)$ upwards, add constant from outside of the function, i.e. $y=f\left(x\right)+c$ .

Therefore, option $\left(B\right)$ is incorrect.

Option (C)

To shift a graph left, add inside to the function's argument .

For a function $y=f\left(x\right)$ , add $c$ units inside to the function's argument i.e. $y=f(x+c)$ .

Therefore, option $\left(C\right)$ is incorrect.

Hence, option (D) is correct.