QuestionWhich of the following describes the polynomial function? The function has a negative leading coefficient. The function has an even degree. The function has zero turning points. The function has one -intercept.
Studdy Solution
STEP 1
1. The graph is a parabola, which indicates a quadratic function.
2. The parabola opens upwards, suggesting the leading coefficient is positive.
3. The vertex of the parabola is at the origin (0,0).
4. The parabola intersects the x-axis at the origin, indicating one -intercept.
5. The parabola is symmetric about the y-axis, indicating an even degree.
STEP 2
1. Analyze the direction of the parabola to determine the sign of the leading coefficient.
2. Determine the degree of the polynomial based on the shape of the graph.
3. Count the number of turning points.
4. Identify the number of -intercepts.
STEP 3
The parabola opens upwards, which means the leading coefficient is positive.
STEP 4
The shape of the graph is a parabola, which is a polynomial of degree 2 (even degree).
STEP 5
The parabola has one turning point at the vertex, which is at the origin.
STEP 6
The parabola intersects the x-axis at one point, the origin, indicating one -intercept.
Based on the analysis, the polynomial function is described as follows:
- The function has a positive leading coefficient.
- The function has an even degree.
- The function has one turning point.
- The function has one -intercept.
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