Question 145·Easy·Nonlinear Functions
Which choice is the -coordinate of the vertex of the parabola shown?
For a quadratic graph, the vertex is the turning point. First decide whether the parabola opens up or down (here it opens up), then locate the lowest point and read its coordinates from the grid. Since the question asks only for the -coordinate, you only need the horizontal position of that point.
Hints
Find the lowest point
Because the parabola opens upward, the vertex is the lowest point on the curve.
Use the grid
Line up the vertex vertically with the -axis ticks to read the -coordinate.
Ignore other points
The -intercept and -intercepts are not needed; you only need the turning point.
Desmos Guide
Enter three clear points from the graph
In Desmos, click to create points that match three easy-to-read points on the parabola (for example, the vertex and two symmetric points at the same height).
Fit a quadratic to the points
Type y1 ~ a x^2 + b x + c to do quadratic regression using your points.
Compute the vertex -coordinate
Use the regression values of and and compute . Choose the option that matches this -value.
Step-by-step Explanation
Identify the vertex on the graph
The parabola opens upward, so its vertex is the lowest point on the curve.
Read the -coordinate
From the grid, the lowest point is directly above .
Therefore, the -coordinate of the vertex is .