Final answer:
The function f(x) = -3(x+2)² +1 is a downward-opening parabola translated left by 2 units and up by 1 unit. It could be further analyzed by completing the square or using the quadratic formula to find the x-intercepts or vertex.
Step-by-step explanation:
The function f(x) = -3(x+2)² +1 represents a transformed quadratic equation. To analyze or graph this equation, we can see that it is a parabola that opens downward due to the negative coefficient in front of the squared term. The term (x+2)² shows that the parabola is shifted to the left by 2 units due to the positive 2 inside the parenthesis. Additionally, the +1 at the end indicates that the graph is shifted upward by 1 unit.
If we are talking about another transformation mentioned in the examples, like completing the square or using the quadratic formula, these processes allow us to solve for the x-intercepts or find the vertex of the quadratic function. Completing the square could convert f(x) = ax² + bx + c to a form that easily reveals the vertex. The quadratic formula, -b ± √(b² - 4ac)/(2a), is used to find the x-intercepts by solving for x when f(x) = 0.