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

Question

Allison says the graph can have 1 x-intercept.
Carson says the graph can have no x-intercepts.
Dolly says the graph can have two x-intercepts.
Erica says the graph can have, at most, 1 x-intercept.
How many of Tom's friends are right and why?
(1 point)

Answer 1

Allison, Dolly, and Erica are correct.

Allison is correct because a quadratic function can have at most 1 x-intercept when the vertex of the parabola lies on the x-axis.

Dolly is correct because a quadratic function can have two x-intercepts if the parabola intersects the x-axis at two points.

Erica is also correct because if the parabola opens upwards, it will not intersect the x-axis and therefore have no x-intercepts.

Carson is incorrect because a quadratic function can have either 0, 1, or 2 x-intercepts.