Answer:
f(x) = -4x² + 48x - 129
Explanation:
Given the quadratic function in vertex form, f(x) = -4(x - 6)² + 15:
In order to transform the given function into its standard form, f(x) = ax² + bx + c, expand the squared binomial (without distributing -4 and adding 15).
f(x) = -4(x - 6)² + 15
f(x) = -4(x² - 6x - 6x + 36) + 15
Combine like terms:
f(x) = -4(x² -12x + 36) + 15
Distribute -4 into the parenthesis:
f(x) = -4x² + 48x - 144 + 15
Combine the constants:
f(x) = -4x² + 48x - 129 ⇒ This is the quadratic function in standard form where a = -4, b = 48, and c = -129.