Worksheet Answers.
3. Flip absolute x first across the x-axis, then move 3 right and 4 up.
4. Flip the figure first across the x-axis, them move it 2 left and 3 down.
6. a) f(4) = 4^2 + 3(4) = 16 + 12 = 28......................b) g(4) = 2(4) - 5 = 8 - 5 = 3
c) f(-2) = (-2)^2 + 3(-2) = 4 - 6 = -2.......................d) If f(x) = 0, then 0 = x^2 + 3x
........................................................................................ Factoring: 0 = x(x + 3) which give you x = 0 or x = -3
7. a) 2(x - 3) + 5( x + 1) = 8........................................... b) 5(3x + 1) = 2(2x - 3) Cross multiply
2x - 6 + 5x + 5 = 8...........................................................15x + 5 = 4x - 6
7x - 1 = 8........................................................................... 11x = -11
7x = 9
x = 9/7....................................................................................x = -1
c) (x + 5) (x - 2) = 0 Factor....................................d) This can be factored to (3x + 1)(2x - 3) = 0
so x = -5 or 2......................................................................so x = -1/3 or 3/2
...................................................................................You could have used the quadratic formula if you wish.
9. From the final answer of 8, the parabola moved 5 to the left and 27 down.
10. Answers for 10 are hard to type, so the will be on the board on Wednesday for you to take a picture of.
- Domain: x is greater than or equal to -5 and smaller than 6 Range: y goes from -5 to 5
- Domain: All x greater than or equal to -4 Range: All real numbers
3. Flip absolute x first across the x-axis, then move 3 right and 4 up.
4. Flip the figure first across the x-axis, them move it 2 left and 3 down.
- f(x)=3(x + 4)^4 + 2 Note: the ^ tells you that the 4 is the exponent this is true for all problems below
6. a) f(4) = 4^2 + 3(4) = 16 + 12 = 28......................b) g(4) = 2(4) - 5 = 8 - 5 = 3
c) f(-2) = (-2)^2 + 3(-2) = 4 - 6 = -2.......................d) If f(x) = 0, then 0 = x^2 + 3x
........................................................................................ Factoring: 0 = x(x + 3) which give you x = 0 or x = -3
- g(6) = 2(6) - 5 = 12 - 5 = 7 f(7) = 7^2 + 3(7) = 49 + 21 = 70
7. a) 2(x - 3) + 5( x + 1) = 8........................................... b) 5(3x + 1) = 2(2x - 3) Cross multiply
2x - 6 + 5x + 5 = 8...........................................................15x + 5 = 4x - 6
7x - 1 = 8........................................................................... 11x = -11
7x = 9
x = 9/7....................................................................................x = -1
c) (x + 5) (x - 2) = 0 Factor....................................d) This can be factored to (3x + 1)(2x - 3) = 0
so x = -5 or 2......................................................................so x = -1/3 or 3/2
...................................................................................You could have used the quadratic formula if you wish.
- y = x^2 + 10x - 2 half of 10 is 5...........................Step 1: find h by cutting the center term in half
5 squared is 25............................Step 2: square h to find number to create ( )^2 5 squared is 25
y = x^2 + 10x + 25 - 25 - 2............Step 3: Add the squared number and its evil negative twin
y = (x + 5)^2 - 27.............................Step 4: Create ( )^2 with first 3 terms, then simplify other numbers
9. From the final answer of 8, the parabola moved 5 to the left and 27 down.
10. Answers for 10 are hard to type, so the will be on the board on Wednesday for you to take a picture of.