Question

the graph of a quadratic function, (y = x^2), is reflected over the (x)-axis. which of the following is the equation of the transformed graph?

(y = -x^2)
(y = (-x)^2)
(y = sqrt{-x})
(y = -sqrt{x})

Explanation:

⚡ Using what you learned: combining transformations

Step 1: Identify the transformation rule

A reflection of a function \( y = f(x) \) over the \( x \)-axis negates the output values of the function:

$$ y = -f(x) $$

Step 2: Apply the rule to the given function

Given the parent function:

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

Applying the reflection over the \( x \)-axis:

$$ y = -x^2 $$

Answer:

\( y = -x^2 \)