UNITS ALGEBRA II WORK PACKET ON QUADRATICS

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UNITS ALGEBRA II WORK PACKET ON QUADRATICS

Factoring Practice #1 Algebra II For #1-20, factor each expression completely. Name Date Per 10*3 + i6x2-15* - 24 5* * 3) x2-36 4) x2 + loj: + 24 5) x3-6x2 + 8x \) 2x2-5x + 6) fit x -' 8) x2-13x-30 (' v 5x 3 9) 3jc _ 4 -fcy

11) 3x*-12 12) x2-13) x2-14) 3x2 + 9x - 12 3 -v) 15) A:2 + 22>; + 121 16)4x2 + llx - 15 10 25x2-30x + 9 * - i \>

Factoring Practice #2 Algebra II Name Date Per For #1-20, factor each expression completely. (4 points each) 3X1- -16 3) x2-25 4) x2 + 12X + 32 X "X 6) 4x2 + 20x + 25 10* 7) 3x2-7x 8) x2-7x - 30 v - -(ox 9) 10) 4x2-9 4-3 -fat

11) 2x2-50 fx - 12) *2- -xs] 15) x2 + 20x + 100 16) Sx2 + IQx - 8 * -VM a 17) x2-4x + 8 ^axa- -ft 18) Jgl - 9_ ^+ at*- 3^* ax1-(a-** - Z 7 19) 7x2 -Sx-2 20) 16x2-24x + 9 X -1 7xl -7x <** -> -3.H

Factoring Practice #3 Algebra II Name. Date Per For #1-20, factor each expression completely. (4 points each) 2) 24x3 - I6x + 15x2-10 -/ti -10 3) x2-.4) x2 + llx + 24 7) 2x2 + 3x 5 8) x2-13*+ 30 X ~ I I st7" -5 10) 4x2-25

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Sbloc foq u PocfeviW o * Sdue each Y-±A = 8-8 X - =-0 5(x2-_l"\0 K=±3 x * i 1

Relating Factors to Zeros Name: We know how to graph a quadratic. We know how to find the zeros of a quadratic graphically. We know how to factor a quadratic. Now we will investigate the relationships between these. 1. What are the zeros of the quadratic graphed at the right? 2. What is the equation of the parabola graphed at the right? 3. What is the equation of the parabola in standard form? r x 4. What is the factored form of the quadratic? u 5. How are the zeros related to the factors? a/e 6. The factored form of a quadratic is (x + \](x - 3). a. What are the zeros of the quadratic? X--lt3 b. What is the equation of the quadratic in standard form? u -x^c. Graph the quadratic using your calculator. d. What are the x-intercepts of the quadratic?

7. The zeros of a quadratic are -4 and 2. a. What are the factors of the quadratic? b. Graph the quadratic (assuming that a = 1). c. Write the equation of the quadratic in vertex form. U d. Write the equation of the quadratic in standard form. e. Factor your equation from part d. Is it the same as your answer to part a? 8. The equation of a quadratic is y a. Factor the quadratic. (J u*. = -2x2 -\2x-\, - X b. What are the zeros of the quadratic? c. Graph the quadratic.

Practice w/relating Factors to Zeros rind the zero(s) of each quadratic function graphically. State the factors and write the equation of f(x). 1. \' f 2. Zeros Factors Equation Zeros Factors Equation Given the following roots of a quadratic function, state the factors. 3. 9, -4 4. -6, -8 5. 0, -5 6. 7 Given the factored form of a quadratic, what are the zeros? 7. f(x)=(x-10){x+l) 8. f(x)=x(x+9) 9. f(x)=(2x+5)(x-l) 10. y=(5x)(x-7) * I 2* j Write the quadratic equation given the following zeros. 1 - t*uchye«l UV/K J 11. 7,-5 12.-8,2 13. 0,6 14. -2,0 15. -4 V) Sketch a graph given the zeros or factors of a quadratic equation. 16. 1,-4 17. -7, 3 18. (x-2)(x+4) 19. x(x+5) w Zeros: Zeros:

Sketch a graph that could represent a quadratic function given the zeros. 20. 4,5 21. yz,-5 L HW-> 4-H- 22. 0,-3 23.-2 Sketch a graph that could represent the given quadratic function written in factored form. 4. (x+4)(x-6)=0 XV. 25. x(2x+3)=0 I 26. (x-4)(x-4)=0 Zeros Zeros x--o, Zeros Use the information provided to write the vertex form of each parabola. 21. v = x2-2x-5 28. y = 29. v = x- r ( t to) * 210. v = 4x2-24^-3 31. = 32. y = 3x2 4> 3 -V^

Name Class Date Practice 10-4 Solving Quadratic Equations Solve each equation by finding square roots. If the equation has no real solution, write no solution. If the value is irrational, round to the nearest hundredth. 1. x2 = 16-144 = 0 4. x2 + 16 = 0 2 + s = - to 5. x = 12 8. 3.x2 = 300 10. x2 = 80 c2-10 = 15 13. x2 = 300 14. 4.r2 + 9 = 41 JOr2 + 8 = 72 17. 4.x2 + 6 = 7 19. Sx2 + 20 = 30 (2<j) je2 + 6 = 17 22. It2-7 = 74 9.x2 = 1 28..r2 = 9 23) x2 + 1 = 0 26. x2 + 4 = 4 29. Sx2-980 = 0 q IS 4.T2-2 = 32. 302-75 = 0 34. 2*2-10 = -4 Qs) 4JC2 + 3 = 3 37. 7X2 + 8-15 38. x2 + I =26 40. x2-400 = Ol 41. T*2-8 = 20 43. 5x2 + 25 = 90 44. x2 + 4X2 = 20 46. 3.x2 -.t2 = 10 47. Zc2 + 6 - ^c2 = 9 49. -3 + 4X2 = 2 50. 7.x2-1008 = 0 Solve each problem. If necessary, round to the nearest tenth. 52. You want to build a fence around a square garden that covers 506.25 ft. How many feet of fence will you need to complete the job? 53. The formula A = 6s2 will calculate the surface area of a cube. Suppose you have a cube that has a surface area of 216 in.2. What is the length of each side? 54. You drop a pencil out of a window that is 20 ft above the ground. Use the formula V = 64s, where V is the speed and s is the distance fallen, to calculate the speed the pencil is traveling when it hits the ground. I 55. Suppose you are going to construct a circular fish pond in your garden. You want the pond to cover an area of 300 ft2. What is the radius of the pond? \1, 56. During the construction of a skyscraper, a bolt fell from 400 ft. What was the speed of the bolt when it hit the ground? Use V2 = 64s.

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Fi nd the value of the discriminant and describe the nature of the roots (real, imaginary, rational, irrational) of each quadratic equation. Then solve the equation. 10. x2 + 10* = -25 11.2x2 = 72 12. x2 + * - 5 = 0 13. x2 + Sx+ 10 = 0 16. x1 + 12* + 32 = 0 17. Zx2-12* + 18 = 0 18. x2-4x + 1 = 0 19. 3X2 + 5x - 2 = 0 20 x2-2x + 5 = 0

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The Quadratic Formula and the Discriminant -ftp- Nature of Roots of a Quadratic Equation Discriminant i?j - 4ac > 0 t>2-4ac = 0 b' - 4ac < 0 Nature of Roots two distinct real roots one distinct real root no real roots Find the value of the discriminant and describe the nature of the roots of each quadratic equation. Then solve the equation^* -l tjog-^- -* 5. m2-8/n = -14 6. p2 + 12p = -4 8. -262 + 6-5 = 0-1 1 JO)7--

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