University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

388

Pages:

3
Author:

Whitney Ford

Algebra II Second Semester Exam Review #3 (Chapter 7 and 8) Name I. Functions. Given: f(x)=3x+1, g(x)=x-2, and h(x) = x²+2. Find: 1) f(-1) 3(4)+1 -341 Write an equation for the inverse,f(x), of f(x) = 2 f(x)=x+2 2) g(2)-h(4) 3) h(g(-3)) (2-2)-(4²+2) (-3-2) 8 y=x+2 hts) = (5)²+2 M=3x-5 x=zy+2 x-2=릇y 27 Solve each of the following functions by synthetic division (get the first root from the calculator). 5) f(x)=2x-5x2-14x+8 -212-5-14 8 4-418-8 2-94 6) f(x) = x²-4x2+3x-12 411 -4 3-12 ↓40 1 03 (x+2) (2x²-2x+4)=0 2,2,43 (x-4)(x²+3)=0 (x+ 7)(x)=x²+x²-3x-6 211-3 2 X=-3±√9-4(13) x=±√3 2(1) x=±√3 个 3 b 3 (x-2)(x²+3x+3)=0 6 2 x=-3 24,±√33 X=-3±13 2 Graph and give the vertex, domain, and range. 8) f(x)=(x-2)²+1 9) f(x)=-x+1+33240) y=√x+6-4 Vertex: (2,1) Domain: Range: 18 (13) Vertex: Domain: Range:3 Vertex: (-6)-4) Domain:6) Range: 40011) From the parent absolute value function, f(x)=x, write the equation that will produce functions with graphs related to the graph of f(x) in the following ways: a) Translated 3 units to the left, flip y=x+3 b) Translated 2 units to the right and 3 units down y = x-21-3 c) Wider by translated up 2 units, flip 2 y=x+2 d) Narrower by factor of 5 and 1 unit to the left y=5/x+11 X Find the vertex for each of the following functions and describe the transformation of the graph from the parent function, f(x)=√x. Then state the domain and range 12) f(x)=√x-6+4 4 13) f(x)=--√x+2-6 Vertex: (64) Domain: t Vertex: (-2-6) Domain: 2 Range: 4 Range: Transformation in words: eft 2 Transformation in words: right 6 dewn 6 fup II. Conics State the center and radius of each circle then graph. If an ellipse, give all necessary information. 1) (x-5)² (-2)2 + 9 25 =1 9:5 b=3 Center (5,2) C2:25-9 vertices (22) 82 (2216 (57) 15-3) foci (5,2+4) = (56) (5-2) length of major axis 2(5) 10 2)x²+y²-10x-12y+45=0 Center: (5,6) Radius: 4 +25 +25 x²-10x+y²-12y (x-5)²+(y-6) = 16 Graph the following parabolas. Find the equation in graphing form if necessary. Find the coordinates of the vertex, p-value, direction of parabola, coordinates of focus, equation of the directrix, and equation of the axis of symmetry. 3) y=(x-3)²-5 12 p=3 dem Vertex: (3,5) P=3 Direction: Awn Focus: (3-8) Directrix: 4-2 AOS: X 3 4)x²-8y-48-0 2 + Equation in graphing form: 2 y=x²-6 Vertex: (076) p=2 Direction up Focus: (04) Directrix: y=-8 AOS: X 5) y²-6y+4x-11-0 (y²-by+9 +4x=11+ 4x=-1(4-3)+20 Equation in graphing form x=-4(y-3)²+5 Vertex: (513) p= Direction: ut Focus: (4,3) Directrix: X=6 AOS: y=3 Write the equations for the following parabolas. 6) vertex: (-4, 5) focus: (-4, 2) 9 -2 -4 P-3 7) vertex: (5, 1) directrix: x=3 8) focus: (3, 9) directrix: y=-1- (3) 2 14=(x+4)²+5 y= 20(X-3)²+4 x=(y-1)²+5 Graph the following ellipse or hyperbola and give all information. 9) 4y²-25x-24y-50x-89-0 Graphing Form: center (13) (4-3) 4y²-by+g)-25 (+2x+1) (-1,-2) vertices (-1,8 4(y-3)2-25 4y²-244-25x²-50x= equation of asymptotes y-3=(x+1) 25 (4)-(xh)2 4 y-k==m(xh) foci (-1, 3+√9.)