Name____________________________________ Algebra 2 Fall Semester Review Directions: Answer each question as completely as possible. If you do not have enough space, you may use a separate sheet of paper and attach it. 1) Determine if each relation is function. ____________ ____________ ___________ ____________ 2) For π(π₯) = 2π₯ β 9 and π(π₯) = 10π₯, find π(β3) =__________________ π(π(4)) = __________________ Find the inverse of each function. 3) π(π₯) = βπ₯ + 2 5) Solve the following system of equations: { 1 π (2) = __________________ π(π(β1)) = __________________ 4) π(π₯) = π₯ 2 + 6 4π₯ + 2π¦ = 20 β2π₯ β 2π¦ = 10 βπ₯ β 5π¦ + π§ = 17 6) Solve the following system of equations using matrices. { β5π₯ β 5π¦ + 5π§ = 5 2π₯ + 5π¦ β 3π§ = β10 7) The booster club sold 19 t-shirts, 12 hats, and 8 blankets Monday for $330. On Tuesday, they sold 7 tshirts, 15 hats, and 12 blankets for $400. Wednesday they sold 23 hats for $230. How much is each tshirt, hat, and blanket? 8) Write the system of inequalities for the graph: 9) Graph the system of inequalities on the graph below and list two points in the solution. 1 {π¦ < 3 π₯ + 2 π₯β₯5 Solve the following absolute value equations. 1 10) 3 |5π₯| β 4 = 21 11) |3π₯ β 2| β 6 = β5 Solve the following absolute value inequalities and graph the solution on the number line. 12) |2π₯ β 1| < 7 1 13) |3 π₯| + 5 β₯ 10 State the attributes of the following functions. 14) π(π₯) = 2|π₯ β 3| + 4 15) π(π₯) = β|π₯| β 5 Vertex: ______________ Vertex: ______________ Axis of Symmetry: _______ Max/Min: ___________ Axis of Symmetry: _______ Max/Min: ___________ Domain: _______________ Range: ______________ Domain: _______________ Range: ______________ x-intercept(s): __________ y-intercept: __________ List the transformations of the following function x-intercept(s): __________ y-intercept: __________ 1 17) π¦ = β 2 |π₯ β 3| 16) π¦ = 2|π₯ + 1| + 1 18) Graph and state the attributes to the following quadratic functions. 19) π(π₯) = 2(π₯ β 1)2 20) π¦ = π₯ 2 β 2π₯ + 5 Vertex: ________________ Vertex: ________________ Axis of Symmetry: _______ Axis of Symmetry: _______ Max/Min: ______________ Max/Min: ______________ Domain: _______________ Domain: _______________ Range: ________________ Range: ________________ Write the quadratic function, in vertex form, with the given vertex and passes through the given point. 21) vertex at (β2,5) and passes through (β1,4) 22) vertex at (1,2) and passes through (0,5) Write the quadratic function that passes through the given points. 23) x y -2 39 3 14 5 32 24) {(0, β32), (5, β17), (6, β20)} 25) The given table represents the height of a bottle rocket as it flies up and returns to the ground. Find a quadratic function to model the data as a function of x, time in the air. Use the model to determine the height of the rocket at 3 seconds. Time Height Elapsed (s) 0 2 4 Factor the following expressions. 26) 5π2 π + 10ππ2 27) π¦ 2 β 81 (ft) 5 11 13 28) 2π₯ 2 + 20π₯ + 48 29) What are the solutions? 10π₯ 2 + π₯ = 3 30) Solve using the quadratic formula. 5π₯ 2 + 2π₯ = 11 31) The parabola π¦ = 3(π₯ β 5)2 β 6 has vertex (5, β6). If the parabola is shifted 5 units to the right and up 5 units, what is the equation of the new parabola? Simplify the expression. Write in π + ππ form. 32) (β9 + 7π) β (11 + 16π) 34) If π΄ = [ β2 5 11 ]and π΅ = [ β4 β6 7 β5 ], what is π΄ + π΅? 2 33) (5 β 11π) + (7 β 15π)
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