Graphs of Polynomial Functions — Quiz

Question 3 • Mathematics III

Which graph shows a polynomial function with a negative leading coefficient?

Answer

Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a parabola opening downward is drawn. It passes through (negative 2 comma negative 8) and (3 comma negative 8). It has its vertex at (0 point 5 comma 1 point 8).

Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It passes through (negative 5 point 5, negative 8), (negative 4 comma 3 point 5), (negative 0 point 5 comma negative 8), (4 comma 1), (6 point 2 comma negative 1 point 5) and (6 comma 8)

Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It passes through (negative 6 point 8 comma negative 8), (negative 5 comma 3), (negative 3 comma negative 3) and (negative 1 point 2 comma 8)

Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a parabola opening upward is drawn. It passes through (negative 3 comma 6) and (3 comma 6). It has its vertex at (0 comma negative 3).

Explanation

A polynomial with a negative leading coefficient has a graph whose ends point downward for an even degree, or whose left end points up and right end points down for an odd degree. Choice A is a downward-opening parabola, so its leading coefficient is negative. Choice D opens upward and has a positive leading coefficient.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz