REVIEW WORKSHEET 5.1-­‐5.3, 5.5 REVIEW 5.1: 1. 3. NAME__________________________ GRAPH THE QUADRATIC FUNCTION. LABEL THE VERTEX AND AXIS OF SYMMETRY. y = 6x 2 − 5x +1 2. y = −2x 2 + x +10 2
y = (x − 3)2 + 2 3
4. y = −(x +1)(x + 7) REVIEW 5.2: 5. 7. SOLVE THE EQUATION BY FACTORING. x 2 + x − 30 = 0 8x 2 + 5x − 4 = 2x 2 − 8x +1 6. 25x 2 + 20x + 4 = 0 8. 4x 2 +10x = x 2 − x + 4 REVIEW 5.3: SOLVE THE EQUATION BY TAKING SQUARE ROOTS. 9. 11. 1 2
x = 32 2
10. 2x 2 + 7 = x 2 +12 3(x + 4)2 = 9 12. 1
− (x + 3)2 + 5 = 2 4
REVIEW 5.5: FIND THE VALUE OF “C” THAT MAKES THE EXPRESSION A PERFECT SQUARE TRINOMIAL. THEN WRITE THE EXPRESSION AS THE SQUARE OF A BINOMIAL. 13. x 2 + 24x + C 14. x 2 + 5x + C 15. 4x 2 + 8x + C WRITE THE EQUATION IN VERTEX FORM BY COMPLETING THE SQUARE. DETERMINE THE VERTEX AND AXIS OF SYMMETRY. 16. 3x 2 + 9x −12 = y 17. x 2 + 9x + 6 = y 18. −5x 2 +10x + 20 = y Answers: 1. (5/12, -­‐1/24) x = 5/12 2. (1/4, 81/8) x = ¼ 3. (3, 2) x = 3 4. (-­‐4, 9) x = -­‐4 5. x = -­‐6 x = 5 6. x = -­‐2/5 7. x = 1/3 x = -­‐5/2 8. x = 1/3 x = -­‐4 9. x = ± 8 10. x = ± 5 11. x = −4 ± 3 12. x = −3 ± 2 3 13. c = 144, (x + 12)2 2
14. 5⎞
⎛
c = 25/4, ⎜ x + ⎟ ⎝
2⎠
15. c = 4, 4(x + 1)2 16. 3⎞
75
⎛ 3 75 ⎞
⎛
3⎜ x + ⎟ −
= 0 , ⎜ − ,− ⎟ ⎝ 2
⎝
4⎠
2⎠
4
17. 9⎞
57
⎛ 9 57 ⎞
⎛
= 0 , ⎜ − ,− ⎟ ⎜⎝ x + ⎟⎠ −
⎝ 2
4⎠
2
4
2
2
18. −5 ( x − 1) + 25 = 0 , (1, 25) 2