Final answer:
The given expression represents a quadratic function in standard form. To find the coordinates of f(x), substitute different values of x into the equation and solve for f(x).
Step-by-step explanation:
The given expression f(x)=-3(x+9)²+8 represents a quadratic function in standard form. It can be simplified as f(x)=-3(x²+18x+81)+8. To find the coordinates of f(x), you need to substitute different values of x into the equation and solve for f(x).
Let's take the values of x as -9, -5, 0, and 3 and calculate the corresponding values of f(x):
For x = -9, f(x) = -3(-9+9)²+8 = -3(0)²+8 = -3(0)+8 = 8
For x = -5, f(x) = -3(-5+9)²+8 = -3(4)²+8 = -3(16)+8 = -48+8 = -40
For x = 0, f(x) = -3(0+9)²+8 = -3(9)²+8 = -3(81)+8 = -243+8 = -235
For x = 3, f(x) = -3(3+9)²+8 = -3(12)²+8 = -3(144)+8 = -432+8 = -424