Question

find the values of the absolute maximum and minimum for the following quadratic function. enter dne if the parabola does not have a maximum or minimum value.

Explanation:

Step1: Analyze the parabola's direction

The parabola opens upwards (since it has a U - shape), so it has a minimum value and no maximum value (as it extends to positive infinity).

Step2: Find the vertex (minimum point)

The vertex of the parabola is the lowest point. From the graph, we can see that the vertex has a y - coordinate of 1 (by looking at the grid lines, the lowest point is at y = 1). Since the parabola opens upwards, this is the absolute minimum. The absolute maximum does not exist (DNE) because the parabola goes to infinity as x approaches positive or negative infinity.

Answer:

Absolute minimum: 1
Absolute maximum: DNE