To determine the local extrema (local minimums and maximums) of the function shown in the image, we observe the graph of the parabola.

1. Local minimum: The graph clearly has a vertex at the point $(0, -5)$, which is the lowest point on the graph. Therefore, the local minimum is:

   • $y = -5$ at $x = 0$.

2. Local maximum: The graph does not have any turning points higher than this minimum. As it opens upwards and continues indefinitely in both the positive and negative $x$-directions, there is no local maximum.

Thus, the values of the local extrema are:

• Local minimum: $y = -5$.
• Local maximum: does not exist (DNE).

Do you want further details or have any questions?

Here are five related questions:

1. What is the equation of the parabola given this graph?
2. How do we find the vertex form of a quadratic equation?
3. What are the intercepts of this parabola?
4. How would the graph change if we introduced a negative coefficient to the quadratic term?
5. How can we calculate the axis of symmetry from the graph?

Tip: For parabolas, the vertex is either the highest or lowest point, and it helps determine the nature of the extrema (minimum or maximum).