Final Exam Study Guide Dynamics of Algebra 2. Chapter Section Example

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1 Final Exam Study Guide Dynamics of Algebra Chapter Section Example Chapter What is a function? Properties of a function Is it a function? Explain. Finding the Slope Slope y y m = x x 1 1 Find the slope between two points: (-,) and (4,-8) Writing the Equation of a Line Writing the equation given a word problem A businessman earns a salary of $0 per week and an additional 10% in commission of his sales, c. Write an equation to model the amount of money, s, the businessman earns per week. Write the equation of a line given a point and a slope. y = mx+ b m = ; (,1) Write the equation of a line given a point and a line parallel or perpendicular. - Parallel same slope - Perpendicular opposite reciprocals (flip it and switch it) Point: (,1) Line parallel to y = 5x+ 5 Point: (,1) Line perpendicular to 1 y = x+ 5

2 Write the equation of a line given a graph. Absolute Value Equations Find the vertex. y = a x h + k Vertex :( h, k) Slope : a y= x 5 + Vertex : Chapter Solving a system of Equations - Substitution o Solve for the lonely variable. - Elimination o Pick a variable, get same number, different signs. - Graphing o Intersection of two lines is your answer. o Word problems like the cell phone project (which is better plan and when?) Cases: - One Solution: Intersecting Lines - Infinitely many solutions: Coinciding Lines - No Solution: Parallel Lines Word Problems 4x 6y = 1 x+ y = 6 The senior classes at High School A and High School B planned separate trips to the county fair. The senior class at High School A rented and filled 11 vans and 6 buses with 510 students. High School B rented and filled 5 vans and buses with 194 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

3 Linear Inequalities - Slope intercept form - Standard form Get into slope-intercept form >,< : dotted, : solid y< x y x+ Chapter 5 Different Forms Vertex form: y= a( x h) + k Standard form: y= ax + bx+ c Intercept form: y= a( x p)( x q) y= x+ 1 1 in? What form is ( ) What form is y x x = + 5 1in? What form is y ( x )( x 4) = + in? Graphing Roles of a, h, k a : shaper, up/down, wide/narrow h : horizontal shift k : vertical shift Describe the graph using a,h, and k. ( x ) y= + 1 1

4 Graph y= x+ 1 1 Graph: ( ) 1. Find the vertex.. Graph using the a-table a = 1a 1(-) - Right one, down a (-) -6 Right one, down 6 5a 5(-) -10 Right one, down 10 Graph: y= x x+ 4 1 Find the vertex: Vertex form ( hk, ) Standard form b Vertex : x = a plug in to equation to solve for y Find the vertex: ( x ) y= y= x x+ 4 1

Vertex standard form - Open up the present - FOIL ( x ) y= 1 + Converting Intercept standard form - FOIL ( )( ) y = x 1 x 4 Relating a graph to zeros (x Intercepts) Estimate the real zeros of the

5 Vertex standard form - Open up the present - FOIL ( x ) y= 1 + Converting Intercept standard form - FOIL ( )( ) y = x 1 x 4 Relating a graph to zeros (x Intercepts) Estimate the real zeros of the function graphed below. Round to the nearest whole number. Graphs of Zeros Number of solutions and intercepts - 1 real solution 1 x-intercept - real solutions x -intercepts - No real solutions 0 x -intercepts Sketch a graph with one solution. Sketch a graph with zero solutions. Sketch a graph with two solutions.

6 Old School/Difference of squares Factor: x + 1x+ x 64 Factoring 4x 5 Solving quadratic equations What are the solutions/x-intercepts to the equation? x 11x+ 10= 0 Radicals - Simplify 4 18 Solve for the x-intercepts using radicals. x + 10= 90 Quadratic Formula ± x = b b 4ac a Find the zeros. x + 4x = 0 Solving quadratic equations for x intercepts

7 Chapter 6 Exponents Exponents ( 4x ) - simplifying xz y 0 4 Adding/subtracting Add/Subtract and write in standard form: ( x 4x+ ) + ( x 4 + x) (x + 4x+ ) ( x 4 + x) Polynomials Dividing using synthetic division (x + 4x x+ ) ( x 1) Graphing End Behavior Sketch the graph of the equation: y= x + x x+ 4 Describe the end behavior: as x + as x Describe the end behavior: as x + as x x + means as you move to the right x means as you move to the left f(x) means the graph 4 y= x + 4x + Describe the end behavior: as x + as x

8 Vocabulary - Leading Coefficient - Degree - Constant Name the leading coefficient, degree, and constant of the polynomial shown below: x + 4x x+ Chapter 7 Exponential Radical Notation with coefficients /4 x Radical Notation Exponential ( ) 4 x Find the inverse y = x Composition of functions f( x) = x+ 1 gx ( ) = x+ 1 Simplify f ( g() x ) Rational Exponents Simplify g( f() x ) Solving radical equations x 1 = x x + 1=

9 Chapter 8 Evaluate log4 64 Converting - exponential log - log exponential 5 Convert to logarithmic: = Convert to exponential: log 9 = Logs Condense Write as a single logarithmic expression: log x log y Expand Expand: log xy z Exponential Functions Word Problems Classify as Exponential Decay/Growth and identify the growth factor. t A= a( 1+ r) Growth = ( ) 4 t ( 1 ) A= a r Exponential Growth Exponential Decay Decay = Compounded Interest n= quarterly = monthly = weekly = daily= Continuously Compounded Interest 4 Classify as Exponential Decay/Growth. 1 x y = t ( 1 ) t ( 1 ) A= a + r A= a r r A= P 1+ n A= Pe rt nt

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28} Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the