A minimum value on a graph is the lowest output, not the input where it happens. For an upward-opening parabola, find the bottom of the curve and read its vertical coordinate. If that point is already visible, reading the graph is faster than rebuilding it in Desmos. Don't swap the coordinates or use an intercept instead.
Hints
- Hint 1
A minimum value means the smallest output of the function. On a graph, outputs are heights measured along the vertical axis. Which point on the curve has the lowest height?
- Hint 2
The vertex is the turning point of a parabola. Because this parabola opens upward, its vertex is at the bottom of the curve. Read that point's vertical coordinate, not its horizontal coordinate.
Step-by-step
Read the lowest point
Step 1Find the point that gives the minimum
No Desmos needed. The lowest point is already visible on the graph.
A minimum value is the smallest output, or height. Since this parabola opens upward, its vertex, the point where it turns, is the lowest point. Look there rather than where the curve crosses an axis.
- Step 2
Read the output at that point
The vertex is , which means . The first coordinate, , tells you where the minimum happens; the second coordinate is the value. For a minimum value, read the height, not the input. So the minimum value of is . Choice A.