SUMMARY
The vertex of the function f(x) = -3(x-2)² - 3 is definitively located at the point (2, -3). This conclusion arises from the vertex formula, which indicates that the vertex is determined by the expression (x-h), where h represents the x-coordinate of the vertex. In this case, substituting x = 2 results in f(2) = -3, confirming that (2, -3) is the maximum point on the graph, as any deviation from this x-value yields a lower function value.
PREREQUISITES
- Understanding of quadratic functions and their standard forms
- Familiarity with vertex form of a quadratic equation
- Knowledge of the properties of parabolas
- Basic algebraic manipulation skills
NEXT STEPS
- Study the vertex form of quadratic equations in detail
- Learn how to derive the vertex from different forms of quadratic functions
- Explore the graphical representation of parabolas and their vertices
- Investigate the effects of coefficients on the shape and position of parabolas
USEFUL FOR
Students studying algebra, mathematics educators, and anyone seeking to understand the properties of quadratic functions and their graphical representations.