Final answer:
A quadratic function is a function of the form f(x) = ax² + bx + c. Given the equation f(x) = (1/3)x² - 3, we can find its solutions using the quadratic formula.
Step-by-step explanation:
A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. In the given equation f(x) = (1/3)x² - 3, we can identify that a = 1/3, b = 0, and c = -3.
To find the solutions to the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values into the formula, we get:
x = (-0 ± √(0² - 4(1/3)(-3))) / (2(1/3))
Simplifying further, we have:
x = ±√(0 + 4) / (2/3)
x = ±2/√3