Question

The degree of the polynomial function f(x) is 4.

The roots of the equation f(x)=0 are −6 , −2 , 1, and 3.

Which graph could be the graph of f(x) ?




A fourth degree function graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 2. The vertical y-axis ranges from negative 200 to 200 in increments of 40. A W-shaped curve with turning point at begin ordered pair 0 comma 180 end ordered pair is graphed. Moving from left to right, the graph decreases through the second quadrant and enters the first quadrant through begin ordered pair 0 comma 180 end ordered pair. It decreases through begin ordered pair 1 comma 0 and enters the fourth quadrant. It decreases and turns upward through begin ordered pair 1.399 comma negative 8.832 end ordered pair and enters the first quadrant through begin ordered pair 2 comma 0 end ordered pair. It turns downward through begin ordered pair 2.544 comma 6.618 end ordered pair. It decreases through begin ordered pair 3 comma 0 and enters the fourth quadrant. It decreases and turns upward through begin ordered pair 5.057 comma negative 120.286 end ordered pair. It increases and enters the first quadrant through begin ordered pair 6 comma 0 end ordered pair and exits the first quadrant.




A fourth degree function graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 2. The vertical y-axis ranges from negative 200 to 200 in increments of 40. A W-shaped curve with turning point at begin ordered pair 0 comma 180 end ordered pair is graphed. Moving from left to right, the graph decreases through the second quadrant and enters the third quadrant through begin ordered pair negative 6 comma 0 end ordered pair. It turns upward through begin ordered pair negative 5.057 comma negative 120.286 end ordered pair. It increases through begin ordered pair negative 3 comma 0 and enters the second quadrant. It increases and turns downward through begin ordered pair negative 2.544 comma 6.618 end ordered pair and enters the third quadrant through begin ordered pair negative 2 comma 0 end ordered pair. It turns upward through begin ordered pair negative 1.399 comma negative 8.832 end ordered pair. It increases through begin ordered pair negative 1 comma 0 and enters the second quadrant. It increases and enters the first quadrant through begin ordered pair 0 comma 180 end ordered pair and exits the first quadrant.


A fourth degree function graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 2. The vertical y-axis ranges from negative 200 to 200 in increments of 400. A W-shaped curve with turning point at begin ordered pair 0 comma 36 end ordered pair is graphed. Moving from left to right, the graph decreases through the second quadrant and enters the third quadrant through begin ordered pair negative 6 comma 0 end ordered pair. It turns upward through begin ordered pair negative 4.572 comma negative 154.96 end ordered pair. It increases through begin ordered pair negative 2 comma 0 and enters the second quadrant. It increases and turns downward through begin ordered pair negative 0.603 comma 45.546 end ordered pair and enters the first quadrant through begin ordered pair 0 comma 36. It decreases and enters the fourth quadrant through begin ordered pair 1 comma 0 end ordered pair. It turns upward through begin ordered pair 2.175 comma negative 33.085 end ordered pair. It increases and enters first quadrant through begin ordered pair 3 comma 0 and exits the first quadrant.


A fourth degree function graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 2. The vertical y-axis ranges from negative 200 to 200 in increments of 40. A W-shaped curve with turning point at begin ordered pair 0 comma 36 end ordered pair is graphed. Moving from left to right, the graph decreases through the second quadrant and enters the third quadrant through begin ordered pair negative 3 comma 0 end ordered pair. It turns upward through begin ordered pair negative 2.175 comma negative 33.085 end ordered pair. It increases through begin ordered pair negative 1 comma 0 and enters the second quadrant. It increases and enters the first quadrant through begin ordered pair 0 comma 36 and turns downward through begin ordered pair 0.603 comma 43.546 end ordered pair. It decreases and enters the fourth quadrant through begin ordered pair 2 comma 0 end ordered pair. It turns upward through begin ordered pair 4.572 comma negative 154.96 end ordered pair. It increases and enters first quadrant through begin ordered pair 6 comma 0 and exits the first quadrant.

Answer 1

Top-right corner graph.

Explanation:

It's important to remember the roots fo the equation
`f(x)=0` are x-interceptions points.

So, the right graph must be a fourth degree function with interceptions at (-6,0), (-2,0), (1,0) and (3,0).

The image attached shows all given choices. There you would observe that the graph placed at the top-right corner is the right answer, because it has all four given x-interceptions.

Therefore, the right graph is at the top-right corner.

Answer 2

A fourth degree function graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 2. The vertical y-axis ranges from negative 200 to 200 in increments of 400. A W-shaped curve with turning point at begin ordered pair 0 comma 36 end ordered pair is graphed. Moving from left to right, the graph decreases through the second quadrant and enters the third quadrant through begin ordered pair negative 6 comma 0 end ordered pair. It turns upward through begin ordered pair negative 4.572 comma negative 154.96 end ordered pair. It increases through begin ordered pair negative 2 comma 0 and enters the second quadrant. It increases and turns downward through begin ordered pair negative 0.603 comma 45.546 end ordered pair and enters the first quadrant through begin ordered pair 0 comma 36. It decreases and enters the fourth quadrant through begin ordered pair 1 comma 0 end ordered pair. It turns upward through begin ordered pair 2.175 comma negative 33.085 end ordered pair. It increases and enters first quadrant through begin ordered pair 3 comma 0 and exits the first quadrant.

Explanation:

The graph must have x-axis zero crossings at the roots, must have portions in all 4 quadrants, and must have a generally W-shape with the local maximum at about (-0.603, 43.546) — found using a graphing calculator. The other descriptions don't match this.