~ to* vb. X c ^ 5 ± \Hi. 11) Identify the vertex of the parabola y = (x + 3) ) Identify the vertex of the parabola y = 2(x-3)(x + i) -f (- * I

Transcription

1 11) Identify the vertex of the parabola y = (x + 3) +4 12) Identify the vertex of the parabola y = 2(x-3)(x + i) -f (- * I.- -JO _-,_ 13) Identify the vertex of the parabola y = x2-6x +11 v. -to, ^ 14) Write the quadratic function y = -(x + 4)(jc -9) in standard form. 15) Write the quadratic function y = (x + 2) - 3 in standard form ) Solve: 8x2 + 18x + 9 = 0 by factoring. * i 17) Solve: + 2 = 9 by extracting square roots. t 1 ^ X4? z ± X c ^ 5 ± \Hi 18) Solve: 2.x2 + x = 5 by using the quadratic formula. gttc7 4^ - "5" -o ~ to* vb

2 19)Given x2-8x + c A) Find the value of c that makes the expression a perfect square trinomial. B) Then write the expression as the square 20) Find the zeros of / (x) = 4x2-4x - 3 = o - 21) Plot (-3 + 2i) in the complex plane./r 22)Find the absolute value of (-2-i) 23) Simplify (4 + 3/) - (-2 + 4i) 24) Simplify 4i(6-i) - ^4**. - f I 25)Simp.ify(-l+2/)(ll ) Simplify 3i (1- I 4- I

3 27)SimpHfy ~<e - 4 f 4 ^ I <f J 28) Simplify f C 1/5 4-3^ 29) Complete the square in order to convert y = x2-8x + 11 into vertex form. 30) Complete the square in order to convert y = 2x2 + 6x + 1 into vertex form. 31) Evaluate the discriminant of the following and then describe solutions (real/nonreal, different/same) A) jc2-4jc + 10 = 0 V^-fctc r I <=> - f 0 ) (i«j? B) x2 C) *2 32) When an object is dropped, the model h (t) = -16f 2 + /z0 describes the height (feet) of the object as a function of time (seconds). The initial height is represented by h0. If an object is dropped from a height of 320 feet, in how many seconds will it hit the ground? Or -, ((<> +. - o X - -T -- 33) Use the quadratic formula to solve -x +2x = 2. H A 2 X, - 2 o x- ~ \ i 0 Jb1-/* <- /If- 7.^ ^s

4 34) Solve the quadratic inequality x2-6x + 5 <, 0 35) Solve the quadratic inequality 2x2 - Ix + 3 s 0 "3 " 3 ^ 32o -/- ^v '?2* 36) Write a quadratic function in vertex form given vertex (-1,4) and point (-2,2) 44 37) Write a quadratic function in intercept form given ^-intercepts -2 & 1 and point ( -1, -6) 38) Write a quadratic form in^tajndardform given points (0,-%)/, (-l,-5), (2,10) 1 b* - -f»«)!o- «x x)x -J 39)Expand (* + y)2 c 3 40) Factor completely: x2-12* ) Factor completely: 4#2-4x - 3 ) / ^ X ^ 3

5 42) Factor completely: 9x2 + 24x ) Factor completely: 6x2 + 15x + 9 *X* sx + V) 44) Factor completely: 2x ) Factor completely: x3-l -CO ' ( (x -»"\ x% X -fi) J 46) Factor completely: -2x3-4x2-3x ) Factor completely: 81jc ) Evaluate 2IU (hint: use fingers and count to 10 as you keep doubling 2, 4, 8, 16, etc.) ) Simplify x2 -x 50) Evaluate -22

6 51)Evaluate (-2)2 52) Evaluate 2 53) Evaluate (-5)"6 (-5) ~ (- 5 54) Evaluate -4~2 + Ho l\ i 3 55) Evaluate (23)2 56) Evaluate ) Simplify (-3x)3 58) Simplify \21*5 feo

7 59) Simplify <& t 60) Subtract (Sx3-3x2-2x + 9) - (6x2 -x +1) -..3 _ i. 61) Multiply (jc + 5)(5*2+3;t-l) -r 62) Multiply (*- 63) Solve 3x4 + 3x3-6^;2-6* = 0 o C XXC_x.^.^ - i o 64) Divide (x3-3x2 -lx + 6) by (x-4) 4 I I v 65)Divide (x3-3x2 -lx + 6) by (x + 2) -1 -f = 3x3+13x2+2x-8 riven that /(-4)-0

8 67) List all the possible rational zeros of f(x} = 4x3 + 5x2-3 C \ *, 3 68) State the degree of the folio wing polynomial: 3 / «\2 3)(x- 2)3 (x +1) k O6- G/NAA, 69) A third degree polynomial function has zeros of 3 and (2-4i). List the other zero. f 70) Write a polynomial function of least degree that has a lead coefficient of 1, real coefficients, and zeros of 4 and 5i. ** 5 c X * 4- - X ~ 71) Draw a rough sketch of the polynomial function CltC. ^ 4 NtoT ur 72) The graph of a cubic polynomial function has jc-intercepts of -3, 2, and 5. The graph also passes through the point (0,-15). Write the cubic polynomial function in intercept form. -JLI - ~i -/S - 73) Simplify 9 / - (3

9 74) Simplify 32-2/5 75) Simplify 51/2 51/4 - S" 76) Simplify 77) Simplify s- 78) Simplify 3]l25y (assume all variables are positive) 79) Simplify ^5a5foV3 (assume all variables are positive) '. 5r c 80) Simplify 3 v5x5 - jc >40jc2 (assume all variables are positive) 81) Simplify >/8 + >/75 + >/50

10 82)Expand (2 + A/3J ( 83) Multiply (2->/s)(3 + 85) Simplify- rx (2 + V5) 4-86)Let A) Find the composition f(g(x)) B) Find the composition 87) If f (x) = -x5 + -, find the inverse 7'1 (j 6 3 = X ' ; v/w*-* 88) Solved-4 = 0 ^4

11 89) Solve 2*3/2 = ) Solve f * -> r. 3 91) Solve f*-* "V* J^ - * ^ ^ - T - T 1 ^ D.-> * 92)Solve x-4 = r f 93) Simplify and write in radical form: 5x y (assume all variables are positive) 94) Simplify and write using rational exponents: ^21x4y2 (assume all variables are positive) - 3X 95) State the domain andrange of yj=jn(.x - 2) + 5 (viors \t

12 96) State the domain and range of y = 3* ) A town has a population of 75,000 and the population increases 2% every year. Write an exponential growth 98) You purchase a car for $25,000 and the value decreases 15% every year. Write an exponential decay model. r - 99) Just set up Uie equation for the following do not evaluate. You deposit $500 in a bank that pays 0.8% annual interest, compounded quarterly. f\w much money will you h 100) Just set up the equation for the following do not evaluate. You deposit $1000 in a bank that pays 2.5% annual interest, compounded continuously. How much money will you have in 20 years? 101) Simplify

13 102) Evaluate Iog2 (64) = "? a' = <»f ^TlT 103) Evaluate Iog9 27 =? ^ = -b 104) Simplify log, 125* - *! = j 105) Find the inverse of y = ex X = - S / 3 \) Use Iog5 (2)«0.4 and Iog5 (3)«0.7 to appro 107) Condense 108) Expand Iog4 6) -

14 109) Use the change of base formula to express Iog37 in terms of common logarithms. 110) Solve 4*- - ^T^r ~* + 3 o7) >- - * (^x + 's -** - ^ ^ 3- =» 111) Solve 41n(-x) 112) Solve 4* = 11 and report answer in terms of natural logs. To 113) You take soup off the stove at 200 deg F. The kitchen is at 75 deg F. TU r. 4r.u The cooling rate of the soup is r = '05 mn In how many minutes will it take the soup to cool to 100 deg F? ^^Cy': T " /oo c -.os t

15 114) Write an exponential function whose graph passes through (3,18) and (1,2). - b _ ex.- 115) Write a power function whose graph passes through (2,16) and (l,4). b 0 - a. I v> b-? = r' 116) The intensity of light varies inversely as the square of the observers distance from the light source. The light intensity is 9 lumens when the observer is IChneters from the light source. If the observer is 3 meters from the light source, what is the light intensity? X - to X = T r r (oo 117) State the domain and range of y = 118) Given y = 3;r+10jt-8,., find the following: A) Vertical Asymptotes * z B) Horizontal Asymptote - 3

16 2 /") o 119) Given y =, find the following: x-4 A) Vertical Asymptote B) Slant Asymptote 120) ionxc- Simplify i-p 4jc-l (x-*v 121) Add x x-2 _ "i)f -< 122) Simplify: 123) Solve: -±±- + x-1 x-3 x-4x+3-3 -o <** >