Final answer:
To find the correct quadratic function reflected across the x-axis, stretched by 5, and down 4, start with the basic function y = x^2, and apply the transformations step by step.
Step-by-step explanation:
To find the correct quadratic function reflected across the x-axis, stretched by 5, and down 4, we need to start with a basic quadratic function of the form y = ax^2 + bx + c. Let's assume the basic function is y = x^2, and apply the transformations one by one.
- Reflected across the x-axis: When a function is reflected across the x-axis, the sign of the 'a' coefficient changes. So, in our case, it becomes y = -x^2.
- Stretch by 5: Stretching a function by a factor of 'k' horizontally can be achieved by changing the 'a' coefficient to 1/k^2. In our case, k is 5, so the function becomes y = -(1/25)x^2.
- Down 4: Shifting a function vertically can be accomplished by adding or subtracting a constant term. In this case, we are shifting down by 4, so we subtract 4 from the function. Finally, the corrected quadratic function is y = -(1/25)x^2 - 4.