Identify the base function and describe the transformation(s) for f(x) = -4*(3x)^2 + 5

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x) = -4*(3x)^2 + 5

The base function here is f(x) = x^2

With the multiplication of x^2 with 9, the rate at which f(x) changes is 9 times larger. Next, 9x^2 is multiplied by -4, this reverses the value of y for each corresponding value of x and increases the rate at which f(x) changes 36 times that of the original function. By adding 5 to -4*9*x^2 the value of f(x) is always 5 greater than the value of f(x) for f(x) = -4*9*x^2 = -4*(3x)^2

The transformations are displayed in the graph below:

The original function is the graph in black, the next transformation changes it to red, next it changes to yellow and the final transformation changes it to purple.