Describe the transformations of the function. 1. f(x)=4(x-3)^2+19 2. f(x)=(-2)/(3)x^2-25 __ __

## Step 1: Analyze the first function<br />### The function $f(x) = 4(x-3)^2 + 19$ can be analyzed by comparing it to the basic quadratic function $g(x) = x^2$. The term $(x-3)$ inside the square indicates a horizontal shift to the right by 3 units. The factor 4 outside the square represents a vertical stretch by a factor of 4. Finally, the term +19 indicates a vertical shift upwards by 19 units.<br /><br />## Step 2: Analyze the second function<br />### The function $f(x) = \frac{-2}{3}x^2 - 25$ can be analyzed by comparing it to the basic quadratic function $g(x) = x^2$. The factor $\frac{-2}{3}$ represents a vertical compression by a factor of $\frac{2}{3}$ and a reflection across the x-axis due to the negative sign. The term -25 indicates a vertical shift downwards by 25 units.