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Math 096 – Chapters 7, 8 and 3 Section 7.1 – Radical expressions and functions 1) Evaluate radicals 2) Simplify radicals 3) Graphing some basic radical functions 4) Give the domain and range of radical functions Section 7.2 – Rational numbers as exponents 5) Changing from rational exponent to radical 6) Changing from radical to rational exponent 7) Evaluating expressions with rational exponents Section 7.3 – Multiplying radicals with the same index 8) Multiplying radicals 9) Simplifying radicals Section 7.4 – Rationalizing denominators 10) Basic problems on rationalizing denominators Section 7.5 – Adding and subtracting radicals 11) Basic problems on adding and subtracting radicals Sections 7.6 – Radical Functions and Radical equations 12) Determine the domain of a radical function 13) Solve simple radical equations a) Algebraically b) Graphically Section 7.7 – Geometric applications 14) Word problems involving the Pythagorean Theorem Section 7.8 – Complex Numbers 15) Evaluating square roots of negative numbers 16) Simplifying radicals involving square roots of negative numbers 1 Section 8.1 – Quadratic equations - the square root property 17) Solving quadratic equations by using the square root property 18) Solving quadratic equations by using graphs 19) Word problems with quadratic equations Section 8.2 – The quadratic formula 20) Solving quadratic equations by using the quadratic formula Section 8.3 – Applications of quadratic functions 21) Solving formulas 22) Solving word problems involving quadratic functions. (know how to answer all the following question-types algebraically and graphically) a. Label variables with words and units b. Answer questions dealing with the x- and y-intercepts c. Use function to answer questions of the type: given x, find y (find f(#)) d. Use function to answer questions of the type: given y, find x (solve f(x)=#) e. Answer questions dealing with the maximum (or minimum) point f. Graph the function with the calculator and find the minimum/maximum point Section 8.4 – The discriminant – types of solutions of quadratic equations 23) How many solutions and what types of numbers will the solutions be? 24) Write a quadratic equation having the given numbers as solutions Section 8.6, 8.7 – Quadratic Functions and their graphs 25) Given a quadratic functions in the vertex form: y f ( x) a( x h)2 k a. b. c. d. e. f. g. h. Give the coordinates of the vertex. Indicate whether the parabola opens up or down Sketch the graph by hand, and check with the calculator Give the domain of the function Give the range of the function Write the equation for the axis of symmetry Give the maximum or minimum point of the function Give the maximum or minimum VALUE of the function i. Transform the given function to the form y f ( x) ax2 bx c j. k. l. m. Find f(#) using either equation (Given x, find y) Find the y-intercept Give the coordinates of the point symmetric to the y-intercept Find the x-intercepts 2 26) Given the quadratic function in the general form y ax bx c a. Find the x-coordinate of the vertex b. Find the y-coordinate of the vertex c. Write the given function in the vertex form y a( x h)2 k d. Sketch the graph by hand, and check with the calculator e. Write both forms in the calculator and graph to make sure you have no mistakes f. Give the domain of the function 2 g. h. i. j. k. l. m. n. Give the range of the function Write the equation for the axis of symmetry Give the maximum/minimum point of the function Give the maximum/minimum VALUE of the function Find f(#) using either equation (Given x, find y) Find the y-intercept Give the coordinates of the point symmetric to the y-intercept Find the x-intercepts 27) Given the graph of a parabola a. Use the graph to solve the two problem types: i. Given x, find y Find f(#) ii. Given y, find x Solve f(x) = # b. Identify the coordinates of the vertex, and the value of the quadratic coefficient a 2 c. Write the vertex form of the parabola y a( x h) k Section 8.8 28) Use the calculator to sketch scatter-diagrams and find mathematical models involving quadratic functions Section 10.3 – Solving nonlinear systems of equations 29) Solve nonlinear systems of equations a. Algebraically b. Graphically Calculator skills Use the calculator to: a) Find zeros or x-intercepts of a function b) Evaluate functions for given values of x c) Find maximum/minimum values of a function d) Solve equations with the calculator e) Sketch scatter-diagrams and find mathematical models Section 3.1 1) System of linear equations in two variables. 2) Solution of a system of equations 3) Possible number of solutions Intersecting lines, one solution: the coordinates of the point of intersection Parallel lines, no solution Same line, infinite number of solutions: all points on the line are solutions 4) Determine whether the ordered pair is a solution of the given system of equations 5) Solve the system graphically Section 3.2 1) Solving systems of equations algebraically a. By substitution b. By addition or elimination 3