Test 2 Study Guide

Test 2 will cover sections 2.5, 3.1, 3.2, 3.4, 4.1, 4.2, & 4.3. 

Some things to know (this may not be a complete list, you are responsible to know all material which we covered in the sections listed above):

• Graphing piecewise defined functions.
• Solving absolute value equalities.  Solving absolute value inequalities won't be on this test but may be on the final.
• Quadratic Functions: standard form, vertex form, vertex formula.  Other key concepts: leading coefficient, axis of symmetry.  When is the vertex a maximum?  When is it a minimum?  Maximization word problems.
• Quadratic equations: solving, zeros, square root property,
• Know how to solve quadratics by: Completing the square, Quadratic Formula, Factoring, and Graphing
• Discriminant (know the yellow box on pg 180)
• Transformations of graphs: Vertical and horizontal shifts (know the yellow box on pg 34), Vertical/Horizontal stretching and shrinking (yellow boxes pg 200 & 201), Reflections of graphs (yellow box pg 204)
• Polynomials: leading coefficient, degree
• Increasing & Decreasing
• Absolute & Local Extrema
• Symmetry: even & odd functions (don’t get these confused with even and odd degree polynomials).  If f(x) contains terms that have only odd powers then f(x) is odd (and similar statement for even).  Remember, a constant term has even power.
• Solving polynomials graphically: Know how to use the “zero”, “maximum”, and “minimum” features on your calculator.
• Turning points.  Definition on bottom of page 237.
• Know the 2 yellow boxes on the bottom of page 241! (relationship between degree, leading coefficient, end behavior, x-ints, etc.)
• Piecewise defined polynomial functions (won’t be on this test but you’ll need to know for final)
• Division of polynomials: long division and/or synthetic division
• Identifying the quotient and remainder.  Writing polynomials in the form: “dividend = (divisor) x (quotient) + remainder”. 
• Remainder & factor theorems.
• Complete factored form.  (Remember the leading coefficient).
• Multiplicity of zeros.  The higher the multiplicity of a zero, the more the graph levels off at the zero.  Odd multiplicity (crosses x-axis ) vs. even multiplicity (does not cross)