Final answer:
To find the maximum or minimum values of a parabola, identify the vertex using x = -b / (2a) for standard form equations or by reading the vertex point (h, k) in vertex form equations.
Step-by-step explanation:
To find the maximum and minimum values of a parabola, we need to identify the vertex of the parabola. The vertex represents either the highest point (maximum) or the lowest point (minimum) on the graph of the parabola. If the parabola opens upwards, the vertex represents the minimum value. If the parabola opens downwards, the vertex represents the maximum value.
The vertex of a parabola given by the standard form equation y = ax^2 + bx + c can be found using the formula x = -b / (2a). Plug this value of x back into the equation to find the corresponding y value, which will be the maximum or minimum value of the parabola depending on the direction the parabola opens.
Alternatively, if the equation is in vertex form, y = a(x - h)^2 + k, then the vertex is simply the point (h, k), where h is the x-coordinate and k is the y-coordinate of the vertex. From this form, it's straightforward to read the maximum or minimum value directly from the equation.