Answer:
f(x) = -3x² + 12x - 16
Step-by-step explanation:
GIven the quadratic function in vertex form, f(x) = -3(x - 2)² - 4
In order transform this function into its standard form, f(x) = ax² + bx + c
Expand (x - 2)² into its perfect square trinomial: (a - b) ² = a² - 2ab + b²
f(x) = -3(x - 2)² - 4
f(x) = -3[x² - 2x - 2x + 4] - 4
f(x) = -3[x² - 4x + 4] - 4
Distribute -3 into the bracket:
f(x) = -3[x² - 4x + 4] - 4
f(x) = -3x² + 12x - 12 - 4
Combine like terms:
f(x) = -3x² + 12x - 16
Therefore, the standard form is: f(x) = -3x² + 12x - 16
