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Algebra

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Hello. I am trying to solve quadratic functions but I'm having difficulty understanding. Here is my work so far...

y=3x^2 + 12x + 9
12/6 = -2 = y
3(-2)^2 + 12(-2) + 9 = -3
x=0 y=9 (0,9)

Would I just plug in 1 and 2 for x and then reflect it while i'm graphing?

So, if I do that, should it come out...

x=1
-----
y=3(1)^2 + 12(1) + 9
y=3+12+9
y=24 (1,24)

x=2
------
y=3(2)^2 + 12(2) + 9
y=12+24+9
y=45 (2,45)

Would this be correct?

  • Algebra - ,

    you are correct on the points 1,24 and 2,45

    The first part, I do not understand what you were doing.

  • Algebra - ,

    y=3x^2 + 12x + 9

    you are correct that when x = 0, y = 9 so (0,9) is on it

    However I do not know what else you are doing.
    I generally complete the square to find the axis of symmetry
    3x^2 + 12x + 9 = y
    get one by x^2 so divide by 3
    x^2 + 4 x + 3 = y/3
    subtract 3 from both sides
    x^2+4x = y/3 - 9/3 =
    add (half of 4)^2 to both sides
    x^2 + 4 x + 4 = y/3 -9/3 + 12/3
    (x+2)^2 = (1/3)(y+3)
    vertex at (-2, -3)
    vertical axis of symmetry at x = -2

  • Algebra - ,

    Well, I'm trying to find two different points by changing the x value since I need to graph these points and then reflect it. I hope this helps you a little.

  • Algebra - ,

    ok, well reflect it about the line x = -2
    and the bottom is at (-2,-3)
    Your (1,24) and your (2,45) are fine
    so
    first point is the bottom (-2,-3)
    next is your (1,24)
    the reflection of that about x = -2 is
    3 to the left of -2 which is (-5,24)

    next do your (2,45)
    that is four to the right of the line of symmetry so go four to the left of -2 to -6
    so (-6,45)

  • Algebra - ,

    this might help:
    http://www.purplemath.com/modules/sqrvertx.htm

  • Algebra - ,

    and this:
    http://uncw.edu/courses/mat111hb/pandr/quadratic/quadratic.html

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