Algebra 2/Trig Honors
Name___________________________________
Chapter 5 Review Assignment # ______ Find the discriminant of each quadratic equation then state the number and type of solutions. 1) −8n 2 + 2n = 10n + 2
2) 6m 2 − m = −7 + 2m + 5m 2
3) 7k 2 + 8 = −6k + 6k 2
Solve each equation by completing the square. 4) n 2 + 8n − 3 = −10
5) 2 p 2 − 11 p − 6 = −8 + 8 p
Solve each equation by factoring. 6) 8 x 2 + 4 x = 12
7) 4a 3 + 2a 2 − 6a = 0
Factor each completely. 8) 18b 2 − 36b
9) 40n 2 − 52n − 120
Solve each equation by taking square roots. 2
10) 4( x − 2) + 5 = 1
11) 8v 2 − 10 = −76
Solve each equation with the quadratic formula. 12) −4m 2 + 12m − 52 = 5 + 8m − 9m 2
Simplify. 13)
−8 + 3i −8i
14)
−4 − 8i −5 + 9i
15) (−7 + 3i) 2 + (5 + 4i) − (3i) − (6i)
Find the absolute value of each complex number. 16) −2 − 13i
©q gKDuwtJac xSXo9fXtzwxaXr4ee TLbLgCo.y g qA7lnlW drViHg7hTtNsY prGets2eKrDvzeNdN.V h uMMaodlex gwOiltRhR iIjn0fQitniiRtQes jAClxgbe1bNr6as d25.y
17) −4 − i 11
-1-
Worksheet by Kuta Software LLC
18) 20(i) 31
19) 15(i) −17
Graph each number in the complex plane. 20) −3 − 4i
21) −2i
Use the information provided to write the vertex form equation of each parabola. 22) y = 3 x 2 + 36 x + 99
23) Vertex: (−10, −5), Passes through: (−12, −13)
Use the information provided to write the equation of each parabola. 24) Passes through (−6, −25), (−13, −18), and (−8, −13) in standard form.
25) Write a quadratic function whose x intercepts are 1 and −2 and passes through (−5, 3) in intercept form.
26) Solve the inequality algebraically: 2 − x + x + 21 ≥ 9
27) Graph y < x − 3 x − 18 1 2 y≥− ⋅x +4 2
28) A grassy rectangular garden is 20 ft by 28 ft. The grass around the edges of the garden are dug up so a flower bed of uniform width can be built to surround the garden. If the 2 area of the flower bed 252 f t , how wide is the flower bed?
29) A magazine has a circulation of 140,000 per month when they charge $2.50 for a magazine. For each $0.10 increase in price, 5,000 sales are lost. How much should be charged per magazine to maximize revenue? What is the max revenue?
30) A baton twirler tosses a baton into the air. The baton leaves the twirler’s hand 6 ft above the ground and has an initial vertical velocity of 45 ft/sec. The twirler catches the baton when it falls back to a height of 5 ft. For how long is the baton in the air?
31) How long would it take for a penny to drop from a 1450 ft tall building?
2
32) A farmer wants to make a rectangular enclosure using a wall as one side and 90 m of fencing for the other 3 sides. Find the area in terms of x and state the domain of the area function. Find the value of x that gives the greatest area.
©8 8KBuOt5aw HSxoYfatOwRasrae3 PL5LaCC.l O RAllklP 5rqitgkh2tQsZ vrqebsOeZrhvjeddE.M r LM2and1er 5wFiStVh2 TIpnLfTi5nmiatleo 7A6l8gZegbdrmaw Q2t.p
-2-
Worksheet by Kuta Software LLC
Answers to Chapter 5 Review Assignment # ______ 1) 0; one real solution 4) {−1, −7} 3 7) {− , 1,0} 2 i 33 i 33 11) ,− 2 2 15) 45 − 47i 19) −15i
{
}
2) −19; two imaginary solutions 3) 4; two real solutions 2 19 + 345 19 − 345 6) { , 8} 5) { , } 7 4 4 8) 18b(b − 2) 9) 4(2n − 5)(5n + 6) 10) {2 + i, 2 − i}
12) 16) 20)
{
3, −
19 5
}
13) −
3 −i 8
17) 3 3 21)
173 Imaginary
26 38 + ⋅i 53 53 18) −20i
14) −
2
Real
2 23) y = −2( x + 10) − 5
Real
24) y = − x 2 − 20 x − 109
25) y =
27) See solution guide 26) −3 ≤ x ≤ 4 28) 3 ft 31) approximately 9.5 seconds 30) approximately 2.8 seconds 32) Area: (90 − 2 x) x. x = 22.5m; 0 < x < 45
©C 5Kfu5t0at ES7opfktawyafrZeJ KLYLOCM.v X XAnlglM FrcikgXhMtXsr brieKsweRrWvVeZdB.U P IMZaUd6eo jwdiwt8hK rIenJfjiZn7iVt6eH LABlygVePbar9ax 929.z
22) y = 3( x + 6) − 9
Imaginary
-3-
1 ( x − 1)( x + 2) 6 29) $2.65; $351,125.00
Worksheet by Kuta Software LLC
