The vertex is the turning point of a quadratic graph. If the coefficient of is positive, the graph opens upward, so the vertex gives its minimum. Graph the function in Desmos and click the lowest point. Read its vertical coordinate: a point where the graph meets the horizontal axis has output , but it need not be the lowest point.
Hints
- Hint 1
A parabola is the U-shaped graph of a quadratic when the coefficient of is positive. Its lowest point is the vertex, where the curve turns. What feature should you look for on the graph?
- Hint 2
The vertex has two coordinates: the first tells you where the minimum happens, and the second tells you the minimum value. After you click the lowest point, which coordinate answers the question?
Step-by-step
Graph and read the minimum
Step 1Identify the lowest point
The coefficient of is positive (), so the graph opens upward. Its vertex, the point where the curve turns, is its lowest point.
- Step 2
Graph the function
Type in Desmos, then click the curve to reveal its marked points. Look for the point at the bottom, not an -intercept where the curve meets the horizontal axis.
- Step 3
Read the minimum value
Click the bottom marked point. Desmos shows : is the input where the minimum happens, and is the output. For the minimum value, read the vertical coordinate. So the minimum value of is . Choice D.