Merced College; Don Power

 

 

MATH 2 – STUDY GUIDE FOR TEST ON CHAPTER 4

 

4.1       Find the vertex and intercepts and graph a quadratic function.

 

 

4.1       Find an equation that models the height of a ball t seconds after it is thrown and use the equation to determine the maximum height of the object and the time it reaches the maximum height (see 4.1, problems 41-44)

 

 

4.2       List all the possible rational zeros of 3x4+x3+10x2+4x-8.

 

            Follow-on questions:

 

            4.3       Graph the function f(x) = 3x4+x3+10x2+4x-8 using a graphing calculator, and, from the graph, make a hypothesis about the actual roots

 

            4.2A    Test your hypothesis using synthetic division

 

 

4.2, 4.3                        Sketch a possible graph for a fourth degree polynomial that has a y-intercept of 5 and zeros of -3, -2, 1 and 5.  You must label the zeros on your graph.

 

 

4.2       Write an equation of a polynomial with a given set of roots , such as 3, -2, and −5

 

 

4.2A    For f(x) = 6x4 −23x3 + 12x2 + 11x − 6, use synthetic division to find f(1),  f(2), and f(3), and use the results to

            a.         Factor the polynomial completely.

            b.         Find all the roots of the polynomial.

 

 

4.6       Add, subtract, multiply or divide complex numbers.

 

 

4.7       Write an equation of a polynomial with a given set of roots (including a complex root), such as 3, -5, and 4+3i.

 

4.7       The following problems use the same polynomial function f(x)=3x4+x3+10x2+4x-8.

 

            Find all the roots, real and complex, of 3x4+x3+10x2+4x-8.  You must list all the possible rational roots.  Then, you must show the synthetic division for the rational roots, and a non-calculator solution for the complex roots.

 

            Use synthetic division to find f(1),  f(2), and f(3), and use the results to graph the portion of the function from a lower bound to an upper bound.

 

 

 

Return to:  Merced College; Don Power               Updated 10/06/05 by Don Power