Question

F(x)=x^2 horizontal shift of 3 vertical shift of -2 reflected over the x-axis. Write the equation

Answer 1

$f(x) = -(x-3)^{2} -2$ is the required function.

Step-by-step explanation:

We have to find the transformation after the horizontal and vertical shifts and then reflection over the x-axis for the given function.

$f(x) = x^{2}$

If there is a horizontal shift of 3, then the function becomes, $f(x) = (x-3)^{2}$

If there is a vertical shift of -2, then the function becomes, $f(x) = (x-3)^{2} -2$

The function is reflected over the x- axis then the function becomes,

$f(x) = -(x-3)^{2} -2$