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Find the equation of this quartic that goes through the point (0, - 2). ا 3 2 1+ 0 -1 2 -5 -x

Find the equation of this quartic that goes through the point (0, - 2). ا 3 2 1+ 0 -1 2 -5 -x

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 4E
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**Problem Statement:** Find the equation of this quartic that goes through the point (0, -2). **Graph Explanation:** The graph is a smooth curve representing a quartic (fourth-degree polynomial) function. It shows the behavior of the polynomial across a range of x-values from -5 to 6. **Key Features of the Graph:** - The x-axis ranges from -5 to 6. - The y-axis ranges from -5 to 3. - The curve has two turning points, visible around x ≈ -3 and x ≈ 3. - The curve passes through the point (0, -2) as specified. - It starts from the top left, dips down, and then rises towards the center before dipping again slightly and rising back up as it moves towards the right. - The end behavior indicates that as x → ±∞, the graph rises in both directions, common for a quartic function with a positive leading coefficient. **Understanding the Graph:** The objective is to find an equation in the form \( y = ax^4 + bx^3 + cx^2 + dx + e \) that matches the curve and passes through the given point. This graph’s characteristic shape can be used to deduce such a polynomial by considering key points, intercepts, and the graph's symmetry.
Transcribed Image Text:**Problem Statement:** Find the equation of this quartic that goes through the point (0, -2). **Graph Explanation:** The graph is a smooth curve representing a quartic (fourth-degree polynomial) function. It shows the behavior of the polynomial across a range of x-values from -5 to 6. **Key Features of the Graph:** - The x-axis ranges from -5 to 6. - The y-axis ranges from -5 to 3. - The curve has two turning points, visible around x ≈ -3 and x ≈ 3. - The curve passes through the point (0, -2) as specified. - It starts from the top left, dips down, and then rises towards the center before dipping again slightly and rising back up as it moves towards the right. - The end behavior indicates that as x → ±∞, the graph rises in both directions, common for a quartic function with a positive leading coefficient. **Understanding the Graph:** The objective is to find an equation in the form \( y = ax^4 + bx^3 + cx^2 + dx + e \) that matches the curve and passes through the given point. This graph’s characteristic shape can be used to deduce such a polynomial by considering key points, intercepts, and the graph's symmetry.
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