Question

Graph it! 3 Chapter Task The polynomial function \(f(x) = ax^4 - 3x^3 - 63x^2 + 152x - b\) has one of its zeros at \(x = 5\) and passes through the point \((-2, -560)\). What might the graph of \(f(x)\) look like? A. Use the given information to determine the values of \(a\) and \(b\). B. Use the given information to state one of the factors of \(f(x)\). C. Determine all the other factors of \(f(x)\). D. Use the factors to determine the zeros of \(f(x)\). E. Determine the end behaviours of \(f(x)\). F. Determine the \(y\)-intercept of \(f(x)\). G. Use all the characteristics you determined to sketch a possible graph of \(f(x)\). H. Verify your results using graphing technology. Discuss any differences between the graph and your sketch. Task Checklist Did you explain your thinking clearly? Did you justify your answers mathematically? Did you show all work and calculations? Did you check your calculations? Did you label your sketch properly?

          Graph it!
3 Chapter Task
The polynomial function \(f(x) = ax^4 - 3x^3 - 63x^2 + 152x - b\) 
has one of its zeros at \(x = 5\) and passes through the point \((-2, -560)\).
What might the graph of \(f(x)\) look like?
A. Use the given information to determine the values of \(a\) and \(b\).
B. Use the given information to state one of the factors of \(f(x)\).
C. Determine all the other factors of \(f(x)\).
D. Use the factors to determine the zeros of \(f(x)\).
E. Determine the end behaviours of \(f(x)\).
F. Determine the \(y\)-intercept of \(f(x)\).
G. Use all the characteristics you determined to sketch a possible graph
of \(f(x)\).
H. Verify your results using graphing technology. Discuss any differences
between the graph and your sketch.
Task Checklist
Did you explain your
thinking clearly?
Did you justify your answers
mathematically?
Did you show all work and
calculations?
Did you check your
calculations?
Did you label your sketch
properly?

Graph it!
3 Chapter Task
The polynomial function f(x) = ax^4 - 3x^3 - 63x^2 + 152x - b
has one of its zeros at x = 5 and passes through the point (-2, -560).
What might the graph of f(x) look like?
A. Use the given information to determine the values of a and b.
B. Use the given information to state one of the factors of f(x).
C. Determine all the other factors of f(x).
D. Use the factors to determine the zeros of f(x).
E. Determine the end behaviours of f(x).
F. Determine the y-intercept of f(x).
G. Use all the characteristics you determined to sketch a possible graph
of f(x).
H. Verify your results using graphing technology. Discuss any differences
between the graph and your sketch.
Task Checklist
Did you explain your
thinking clearly?
Did you justify your answers
mathematically?
Did you show all work and
calculations?
Did you check your
calculations?
Did you label your sketch
properly?

Added by Elizabeth W.

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