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