Question

Write a quadratic equation as a transformation from f(x)=x² for a function that had a horizontal shift to the right 3, vertical shift down 2, has been reflected over the x-axis along with also having a verticle strech by a factor of 2

Answer 1

The transformed quadratic equation after applying a horizontal shift to the right by 3, a vertical shift down by 2, reflection over the x-axis, and a vertical stretch by a factor of 2 is -2(x - 3)² - 2.

Step-by-step explanation:

When transforming the quadratic function f(x) = x² according to the given transformations, we need to apply the following changes:

• A horizontal shift to the right by 3 units, which is represented by replacing x with (x - 3).
• A vertical shift down by 2 units, which can be achieved by subtracting 2 from the function.
• A reflection over the x-axis, which requires multiplying the function by -1 to invert the output values.
• A vertical stretch by a factor of 2, meaning we multiply the function by 2.

Combining all these transformations, the new quadratic equation will be -2(x - 3)² - 2. To elaborate, the function f(x)=x² becomes -2(x-3)² to account for the reflection and vertical stretch, and then we subtract 2 to account for the vertical shift.