Honors Algebra II

Honors Algebra II Learning Targets for 1st Semester:

Graphing and Transformations:  I can identify families of functions and compare them with their parent functions o Linear, Absolute Value, Quadratic o Polynomial o Radical o Rational  I can describe transformations of parent functions o Translating horizontally and/or vertically o Reflecting over the x-axis o Stretching or shrinking vertically  I can describe combinations of transformations  I can graph quadratic inequalities  I can explain the end behavior of polynomial function  I can use x-intercepts to graph polynomial functions  I can state the domain and range of functions  I can graph rational functions in the form y = ax+b/cx+d

Writing Equations:  I can write functions representing transformations o translations and reflections o stretches and shrinks o combinations of transformations  I can write equations of linear functions using points and slope  I can write equations of quadratic functions using vertices, points, and x-intercepts  I can write the equation of a parabola when given the vertex, focus, or directrix  I can write the equation of polynomial function when given the zeros of the function  I can find linear, quadratic, cubic, and quartic models using a graphing calculator  I can write inverse variation equations

Solving Equations/Inequalities:  I can solve system of linear equations in three variables algebraically  I can solve quadratic equations o Using square roots o By factoring o By quadratic formula  I can solve a system of nonlinear equations  I can solve quadratic inequalities  I can solve polynomial equations o By factoring (Difference/Sum of Cubes, by Grouping, Quadratic Form) o Using Synthetic Division  I can solve equations involving radicals and rational exponents  I can solve radical inequalities Simplifying Expressions:  I can add, subtract, multiply complex numbers  I can add, subtract, multiply polynomials  I can use Pascal’s Triangle to expand binomials  I can simplify expressions with rational exponents  I can simplify radical expressions  I can add, subtract, multiply, and divide functions  I can simplify rational expressions  I can multiply and divide rational expressions

Features of Quadratic Functions:  I can identify properties of parabolas in vertex form, standard form, or intercept form o Finding vertex and Axis of Symmetry o find the maximum and minimum values of a quadratic function o Sketch a graph of quadratic functions o Solve real-life problems involving quadratic functions  I can put a quadratic equation into vertex form by completing the square  I understand the relationship between the focus and directrix of a parabola. o Identify the focus and directrix when given an equation with vertex at the origin o Solve real life problems related to the focus and directrix of a parabola

Features of Polynomial Functions:  I can identify local maximum and local minimum values of polynomial functions  I can determine the intervals where a function is increasing and decreasing

Inverse of Functions:  I can find the inverse of functions  I can determine if the inverse of a function is a function  I can verify inverses of functions by using composition

Other Concepts:  I can use long division to divide polynomials by other polynomials  I can identify even and odd functions  I can use finite differences to determine the degree of a polynomial  I can classify direct and inverse variation