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GeoGebraGeoGebra Classroom

Fourth degree polynom

Task

A fourth degree polynomial function has a maximum at (1, 10) and an inflection point at (4, -1). Furthermore f(x) has a root at x = -3. Compute the values for the coefficients a, b, c, d and k and plot the graph of f(x).

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Instructions

1.Define the function f(x) by entering  into the Input Bar.
2.To compute the values of the five coefficients, set up five equations using the information given above.
(1, 10) is a point on the graph of f(x): Enter the equation into the Input Bar and press Enter.
(1, 10) is a maximum of f(x): Enter the equation into the Input Bar and press Enter.
(4, -1) is a point on the graph of f(x): Enter the equation into the Input Bar and press Enter.
(4, -1) is an inflection point of f(x): Enter the equation into the Input Bar and press Enter.
(-3, 0) is a point on the graph of f(x): Enter the equation into the Input Bar and press Enter.
3.Label the five equations by respectively pressing the More button and selecting Add label.
Note: The equations will be labeled eq1 to eq5.
4.Solve the system of equations by entering into the Input Bar.
5.Use the command to apply this solution to the function and to substitute the parameters a to k by the computed values.
Note: The graph of the function will be displayed in the Graphics View.

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