Question 24 GRAPHIC DESIGN Kassie sketches the function \( f(x)=-1.25(x-1)^{2}+18.75 \) as part of a new logo design. Describe the transformations she applied to the parent function in creating her function. The transformations used to create her function include a reflection in the Select Choice \( v \), a Select Choice \( v \) stretch by a scale factor of 1.25 , a Select Choice \( v \) shift to the Select Choice \( v 1 \) unit, and a Select Choice \( v \) shift Select Choice \( v \) sis.75 units.

To analyze the function \( f(x) = -1.25(x-1)^{2} + 18.75 \) and describe the transformations applied to the parent function \( g(x) = x^2 \), we can break it down as follows: 1. **Reflection**: The negative sign in front of the \( 1.25 \) indicates a reflection across the x-axis. So, there is a reflection in the **x-axis**. 2. **Vertical Stretch**: The coefficient \( 1.25 \) (after the reflection) indicates a vertical stretch by a scale factor of \( 1.25 \). So, there is a **vertical stretch** by a scale factor of \( 1.25 \). 3. **Horizontal Shift**: The term \( (x-1) \) indicates a horizontal shift to the right by \( 1 \) unit. So, there is a **shift to the right** \( 1 \) unit. 4. **Vertical Shift**: The constant \( +18.75 \) indicates a vertical shift upwards by \( 18.75 \) units. So, there is a **shift upwards** \( 18.75 \) units. Putting it all together, the transformations applied to the parent function \( g(x) = x^2 \) to create the function \( f(x) = -1.25(x-1)^{2} + 18.75 \) are: - Reflection in the **x-axis** - Vertical stretch by a scale factor of **1.25** - Shift to the **right** \( 1 \) unit - Shift **upwards** \( 18.75 \) units