A polynomial function has a root of negative 3 with multiplicity 2 , a root of 0 with multiplicity 1 , a root of 1 with multiplicity 1 , and a root of 3 with multiplicity 2 If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?
Answer
A
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 1 passing through(negative 3 point 8 comma 8) crosses x axis at (negative 3 comma 0), goes down and curves up at (negative 2 comma negative 3 point 5), crosses the y axis at (0 comma negative 0 point 8). From here it touches the x axis at (1 comma 0), goes down slightly and again crosses the x axis at (3 comma 0), and moves to quadrant 1 through the point (4 comma 7).
B
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 3, passing through the point (negative 3 point 5 comma negative 8), touches the x axis at (3 comma 0), moves down and curves up at (negative 1 point 8 comma 7), and passes through the origin. From here it moves up slightly and passes through (2 comma 0), goes down, curves up at (2 comma negative 2), crosses x axis once again at (3 comma 0) and moves to quadrant 4 through the point (3 point 5 comma negative 8).
C
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. The graph starts from quadrant 3 passing through the point (negative 3 point 5 comma negative 8), it crosses the x axis at (negative 3 comma 0) moves up and curves down at (negative 2 comma 7), crosses the y axis at (0 comma 1), crosses the x axis at (1 comma 0), moves up and curves down at (2 point 5 comma 1). It then moves down, crosses x axis at (2 comma 0) and moves to quadrant 4 through the point (4 comma negative 8).
D
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from (negative 3 point 8 comma 8), touches the x axis at (negative 3 comma 0), goes up to (negative 1 point 5 comma 3 point 5) and comes down to the origin. From here it goes down slightly and curves up to (2 point 1), curves down to touch x axis at (2 comma 0) and moves to quadrant 1 through the point (4 comma 8).