Which of the following equation describes the quadratic parent function after it has been shifted two units down?

A. y=x^2-2
B. y=-x^2-2
C. y=x^2+2
D. y=-x^2+2

shifting down 2 means you subtract 2 from the y values. So, what do you think?

A quadratic function that has been reflected over the -axis, horizontally stretched by a factor of 7

To describe the quadratic parent function after it has been shifted two units down, we need to subtract 2 from the original equation.

The correct equation is therefore:

A. y = x^2 - 2

To determine the equation of the quadratic parent function after it has been shifted two units down, we need to recall the general form of a quadratic function and understand how shifting affects the equation.

The general form of a quadratic function is y = ax^2 + bx + c. In this case, the parent function is y = x^2.

When a quadratic function is shifted upward or downward, we modify the constant term (c). For a downward shift, we subtract from the constant term.

In the given options:
A. y = x^2 - 2 represents a downward shift of 2 units because we subtract 2 from the constant term of the parent function. This is the equation that describes the quadratic parent function after it has been shifted two units down.

B. y = -x^2 - 2 represents a downward shift but also has a reflection about the x-axis due to the negative sign in front of the x^2 term.

C. y = x^2 + 2 represents an upward shift because we add 2 to the constant term. This does not match the required downward shift.

D. y = -x^2 + 2 represents an upward shift combined with a reflection about the x-axis due to the negative sign.

Therefore, the correct equation describing the quadratic parent function after it has been shifted two units down is A. y = x^2 - 2.