Troy

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Can someone check my answers for the following problems.

Simplify. Assume that no denominator equals 0.
1)(7x^2+3x-9)-(-x^2+8x-3)
answer: 6x^2-5x-6

2) 5x^3(7x)^2
answer: 245x^5

3) (2x-3)^2
answer: 4x^2-9

4) Use synthetic division to find (2x^3-5x^2+7x-1)/(x-1)
answer: 3

5)Identify the vertex,axis of symmetry, and direction of opening for y=2(x+3)^2-5
answer:
Axis of symmetry is x= -3/4
vertex -3/4
opens up

6) write y=-4x^2+8x-1 in vertex form
answer: (-4x+4)^2-17

  • Troy -

    1)(7x^2+3x-9)-(-x^2+8x-3)
    answer: 6x^2-5x-6
    now wait a minute
    7 x^2 - ( -x^2) = 7 x^2 + x^2 = 8 x^2
    agree with -5x-6

    3) (2x-3)^2
    answer: 4x^2-9
    NO
    (2x-3)(2x-3) = 4x^2-12 x + 9

    now if you factor 4x^2 - 9 you get (2x-3)(2x+3)

  • Troy -

    4) Use synthetic division to find (2x^3-5x^2+7x-1)/(x-1)
    answer: 3
    Well I get a remainder of 3
    2x^2 - 3 x + 4 and remainder of 3

  • Troy -

    5)Identify the vertex,axis of symmetry, and direction of opening for y=2(x+3)^2-5
    answer:
    Axis of symmetry is x= -3/4
    vertex -3/4
    opens up
    ===============
    yes, opens up because as |x| gets big, y gets big +
    (x+3) = 0 at x = -3
    That is axis of symmetry
    when x = -3
    y = -5
    so vertex at (-3,-5)

  • Troy -

    6) write y=-4x^2+8x-1 in vertex form
    answer: (-4x+4)^2-17

    y+1 = -4 x^2 + 8 x
    -(y+1)/4 = x^2 - 2x
    complete square by adding (-2/2)^2 to both sides
    -(y+1)/4 + 1 = x^2 -2 x +1
    -(y+1)/4 + 1 = (x-1)^2
    (x-1)^2 = -y/4 -1/4 +4/4
    (x-1)^2 = (-1/4)(y-3)
    vertex (1,+3)

  • Algebra2 -

    For #1-3 I have to simplify them...and for #1 would it be 8x^2-5x-6 in the book it tells me to use the FOIL method.

  • Troy -

    and for #1 would it be 8x^2-5x-6
    Yes

    3) (2x-3)^2
    answer: 4x^2-9

    NO
    (2x-3)(2x-3) = 4x^2-12 x + 9 <--- That is FOIL

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