ALGEBRA 2 MIDTERM TOPICS
 2.6 Special Functions (p. 101-107)
o Graph Piecewise and Step Functions
o Write piecewise functions from given graph
o Evaluate a piecewise function at a given value (i.e. f(2))
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 4.3 Solving Quadratic Equations by Factoring (p.238-245)
o Write quadratic equations from given roots [Given a and b are
roots, (x-a)(x-b)=0, then FOIL]
o Factor Quadratics:
– Factor out GCF
2.7 Parent Functions and Transformations (p. 109-116)
– Perfect Square Trinomials
o Identify parent functions of given functions/graphs (constant, linear,
– Difference of Squares
quadratic, absolute value)
– Trinomials f(x)=ax2+bx+c using Guess/Check Method or
o Determine transformation(s) of functions from parent (using
Grouping Method (product/sum)
equation / graph)
o
Solve Quadratics by Factoring Completely; set each factor = 0 and
o Identify Domain and Range of functions (using interval notation)
solve for x/zeros of function
3.2 Solving Systems of Inequalities by Graphing (p.146-152)
 4.5 Completing the Square (p. 256-262)
o Graph Systems of Inequalities (shade overlapping region)
o Complete the Square to find the value of c (given x2+bx, find
o Identify vertices of overlapping region of system of inequalities
(b/2)2=c)
o Write a system of linear inequalities for a given situation
o Solve an equation by completing the square [factor out a, find c,
3.3 Optimizing with Linear Programming (p.154-160)
write as (x-#)2, take square root of each side (don’t forget ±), then
o Write AND Graph constraints/system of inequalities for given
solve for x]
situation
o Write Quadratic Functions in Vertex Form f(x)=a(x-h)2+k
o Calculate the max/min value using the Objective Function f(x,y)
o Interpret the solution for the max/min value in terms of the problem  4.6 The Quadratic Formula and the Discriminant (p.264-272)
o Solve quadratic equations using Quadratic Formula (simplify
situation
radicals & find complex solutions)
4.1/4.2 Graphing Quadratic Functions & Solving Quadratic Equations
o Calculate the value of the discriminant (b2-4ac)
by Graphing (p. 219-236)
o Use the discriminant to determine the number & type of solutions
o Graph quadratic functions from standard (f(x)=ax2+bx+c) & vertex
[complex, 1 rational, 2 real (rational/irrational)]
form (f(x)=a(x-h)2+k)
o Identify key features of quadratic graphs (vertex, axis of symmetry,  4.7 Transformations of Quadratic Graphs (p. 275-280) 2
o Write Quadratic Functions in vertex form (f(x)=a(x-h) +k) by
max/min value, graphing pattern, domain, range)
completing the square
o Projectile Motion Problems: [4.1-4.2 Continued]
o
Identify Transformations from parent function (f(x)=x2): translations
– Write model using h(t)= –16t2+v0t+h0 for feet and h(t)=up/down/left/right, reflection over x-axis, and vertical
4.9t2+v0t+h0 for meters
stretch/compression or narrower/wider
– Find Max height & Time to reach max height
 4.8 Quadratic Inequalities (p. 282-288)
[Vertex (time, height), use -b to find x-value & plug into h(t)
o Graph Quadratic Inequalities with 2-variables (i.e. y < x2 – 3)
2a
model to find height]
[Graph quadratic (using solid/dashed curve), use test point to shade
– Find when object reaches the ground (set = 0 & use Quadratic
region of solutions (inside/outside)]
Formula)
o Determine if a given value/point is a solution to quadratic inequality
 5.7 Roots and Zeros (p.358-365)
o Find roots/zeros/x-intercepts of given polynomials: use synthetic
division for given zero(s), factor depressed polynomial to determine
remaining zero(s)
o
Graph polynomials using end behavior and ALL zeros with
 5.1 Operations with Polynomials (p.303-309)
multiplicities
o Multiply, Divide & Simplify expressions using Exponent Properties
o Multiply Polynomials using the Distributive Property
 6.1 Operations on Functions (p.385-392)
o Add, Subtract, Multiply and Divide Functions
 5.2 Dividing Polynomials (p.311-317)
o Compose functions [f(g(x)) or g°f (x)]
o Divide polynomials using Long Division
o Identify restrictions on the domain of functions and write in interval
(write remainders as fractions)
notation
o Divide polynomials using Synthetic Division
(4.8 continued)
o Solve Quadratic Inequalities in 1-variable (i.e. x2 –2x – 3 ≥ 0)
[Factor, find zeros, plot on number line using open/closed circles,
determine shaded region(s), answer using interval notation]
(write quotient as polynomial)
 5.3 Polynomial Functions (p. 322-329)
o Write polynomials in Standard Form & Identify Degree and
Leading Coefficient
o Determine End Behavior of polynomials (+ odd, - odd, + even, even using infinity notation)
o From graph of function, determine # of real zeros & end behavior
o Identify zeros and their multiplicity (from graph)
 5.4 Analyzing Graphs of Polynomial Functions (p. 330-337)
o Identify turning points, relative maximums and minimums and
zeros of a function from its graph
o Use Graphing Calculator to find values of zeros & relative
max./min. values
o Identify increasing / decreasing intervals on graph of polynomial
o Identify domain & range using interval notation
 5.5 Solving Polynomial Equations (p.342-349)
o Factor polynomials using GCF, diff of squares, sum/diff of cubes,
grouping, quadratic form
o After factoring, set each factor/piece =0 and solve for all values of x
(real and complex)
 5.6 The Remainder and Factor Theorems (p. 352-357)
o Use synthetic division to determine whether (x – #) is a factor of the
polynomial
o Given a factor/zero of a polynomial, write polynomial in factored
form and find all zeros
 6.2 Inverse Functions and Relations (p.393-399)
o Find inverse relations/functions from given points
o Graph inverse functions/relations
o Find inverse functions/relations from given functions (switch x/y &
solve for y)
o Verify inverses using composition of functions