Version 2 For Questions 182 - Describe each transformation that would occur if the parent function is y=x^2 You can earn: 1 ptson for correctly describing each possible transformation) 1 ptfor using the corroct math terms 1. f(x)=3(x-4)^2-6 2. g(x)=-(1)/(3)(x+3)^2+4 square 18points=

To describe the transformations of the parent function \( y = x^2 \) for each given function, we need to identify and explain the effects of each term in the transformed functions.<br /><br />1. For \( f(x) = 3(x-4)^2 - 6 \):<br /><br /> - **Horizontal Shift**: The term \( (x-4) \) inside the squared term indicates a horizontal shift. Specifically, it shifts the graph 4 units to the right.<br /> - **Vertical Stretch**: The coefficient 3 outside the squared term indicates a vertical stretch by a factor of 3. This means that the graph will be stretched vertically, making it narrower.<br /> - **Vertical Shift**: The term \(-6\) outside the squared term indicates a vertical shift. Specifically, it shifts the graph 6 units downward.<br /><br /> So, the transformations are:<br /> - Horizontal shift 4 units to the right<br /> - Vertical stretch by a factor of 3<br /> - Vertical shift 6 units downward<br /><br />2. For \( g(x) = -\frac{1}{3}(x+3)^2 + 4 \):<br /><br /> - **Horizontal Shift**: The term \( (x+3) \) inside the squared term indicates a horizontal shift. Specifically, it shifts the graph 3 units to the left.<br /> - **Vertical Compression**: The coefficient \(-\frac{1}{3}\) outside the squared term indicates a vertical compression by a factor of \(\frac{1}{3}\). This means that the graph will be compressed vertically, making it wider.<br /> - **Reflection**: The negative sign in front of the coefficient indicates a reflection across the x-axis.<br /> - **Vertical Shift**: The term \(+4\) outside the squared term indicates a vertical shift. Specifically, it shifts the graph 4 units upward.<br /><br /> So, the transformations are:<br /> - Horizontal shift 3 units to the left<br /> - Vertical compression by a factor of \(\frac{1}{3}\)<br /> - Reflection across the x-axis<br /> - Vertical shift 4 units upward