Final answer:
The quadratic function representing a vertical stretch by a factor of 4, horizontal shift left by 7 units, and vertical shift down by 1 unit is f(x) = 4(x+7)² - 1.
Step-by-step explanation:
To formulate a quadratic function with the given transformations, we will apply a vertical stretch factor, a horizontal shift, and a vertical shift to the basic quadratic function f(x) = x². The vertical stretch by a factor of 4 can be achieved by multiplying the function by 4, so f(x) becomes 4x².
To achieve a horizontal shift to the left by 7 units, we replace x with (x+7), making our function 4(x+7)². Finally, to shift the graph vertically downward by 1 unit, we subtract 1 from the function, resulting in 4(x+7)² - 1. Thus, the final form of the quadratic function is f(x) = 4(x+7)² - 1.