Paul is sketching the graph of a quadratic function. He is asking his friends how many x-intercepts his function can have. Below is the feedback from his friends.

Question

1. Allison says the graph can have "1" x-intercept.
2. Carson says the graph can have "no" x-intercepts.
3. Dolly says the graph can have "two" x-intercepts.
4. Erica says the graph can have at most, "1" x-intercept.
How many of Paul's friends are right and why? Select from below the correct answer.

A. 0
B. 1, Dolly is right because a quadratic graph has exactly "two" x -intercepts.
C. 2, Allison and Carson are right because the graph can have "0" or "1" x-intercepts.
D. 3, Allison, Carson, and Dolly are right because the graph can have "0, 1, or 2" x-intercepts.
E. 4, They are all right because the graph can have a varying number of x-intercepts.

Answer 1

D. 3, Allison, Carson, and Dolly are right because the graph can have "0, 1, or 2" x-intercepts.

A quadratic function can have 0, 1, or 2 x-intercepts depending on the position of the vertex relative to the x-axis. Allison is correct that it can have 1 x-intercept if the vertex is exactly on the x-axis, Carson is correct that it can have no x-intercepts if the vertex is above or below the x-axis, and Dolly is correct that it can have 2 x-intercepts if the vertex is below the x-axis. Erica is incorrect in stating that the graph can have at most 1 x-intercept.