Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

For the equation y = 6+6x-(1/3)x^2?

For the equation y = 6+6x-1/3x^2

please help me

graph the equation using the vertex and at least four other points.

I missed this when my teacher taught it. I don't know how it would look on a graph.

However, I think the vertex is f(6)=6+54-27=33

So, please if you have the time show me the graph pf the equation using the vertex and at least four other points.

Thank you very very very very much.

4 Answers

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  • 1 decade ago
    Favorite Answer

    The vertex is f(9) = 33.

    To make the graph, just choose some x values around the vertex (see more info in http://en.wikipedia.org/wiki/Quadratic_equation )

    for example:

    ....x ...........y

    -20 -247.33

    -10 -87.33

    0 6

    9 33

    20 -7.33

    40 -287.33

    I can't paste the figure here with the graph, but it looks like a hill, with the maximum at x = 9

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  • 4 years ago

    You're really careless with signs, I'm saying this firsthand. Assuming the (-) in the beginning of each line is not intended to be a minus symbol. (be careful with that, never use this symbol to mark headlines in math; in fact, don't mark anything at all) (y) for correct and (n) for incorrect I'm gonna save space from the variables, so interpret (1, 2, 3) as x^2 + 2x + 3, etc 1. (3, 4, 1) + (4, 5, -1) = (3 + 4), (4 + 5), (1 - 1) = 7, 9, 0 (n) 2. (6, 5, 3) + (4, 2, -7) = (6 + 4), (5 + 2), (3 - 7) = 10, 7, -4 (n) 3. (6, 11, -7) - (5, 3, -10) = (6, 11, -7) + (-5, -3, 10) = (6 - 5), (11 - 3), (-7 + 10) = 1, 8, -3 (n) 4. (12, 3, 7) - (7, 1, 9) = (12 - 7), (3 - 1), (7 - 9) = 5, 2, -2 (n) You need to know that x^m * x^m = x^(m + n) not x^(m*n) 5. (4x^3)(x^4) = 4(x^3*x^4) = 4*x^(3 + 4) = 4x^7 (n) When multiplying 2 sums, you have to multiply out all the possible pairs, not just the first and last. (a + b)(c + d) = ac + bc + ac + ad 6. (3x + 1)(x - 2) = 3x*x + x - 3x*2 - 1*2 = 3x^2 + x - 6x - 2 = 3x^2 - 5x - 2 (n) 7. (5x - 1)(2x - 2) = 5x*x - 1*2x - 5x*2 + -1*-2 10x^2 - 2x - 10x + 2 = 10x^2 - 12x + 2 (n) Point-slope formula: All the lines with slope m and point (x1, y1), has equation y - y1 = m(x - x1) 8. y - 4 = 3(x + 1) --> y - 4 = 3x + 3 --> y = 3x + 7 (y) 9. y + 3 = 4(x - 2) --> y + 3 = 4x - 8 --> y = 4x - 11 (n) 10. 4x + 3 > 6x - 1 --> 4x - 6x > -1 - 3 --> -2x > -4 --> x < -4/-2 --> x < 2 (n) 11. (4x^2 + 2x + 1)(x - 5) = (4x^2 + 2x + 1)*x - (4x^2 + 2x + 1)*5 = (4x^3 + 2x^2 + x) - (20x^2 + 10x + 5) = 4x^3 + 2x^2 + x - 20x^2 - 10x - 5 = 4x^3 - 18x^2 - 9x - 5 (n) 12. (7x^2 + x + 3)(x - 4) = (7x^2 + x + 3)*x - (7x^2 + x + 3)*4 = 7x^3 + x^2 + 3x - 28x^2 - 4x - 12 = 7x^3 - 27x^2 - x - 12 (y) You'll want to know that (a + b)^2 does not equal a^2 + b^2 (try it out with any integers) 13. (4x + 3)^2 = (4x + 3)(4x + 3) = 16x^2 + 12x + 12x + 9 = 16x^2 + 24x + 9 (n) For quicker calculation use this formula for square of a sum (a + b)^2 = a^2 + 2ab + b^2 You got a total of 2/13. That's not good at all :(

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  • 1 decade ago

    to graph four points,just plug in 4 values for x and see what you get for y each time. those will be your coordinates for four points. the graph should be a parabola. try some x values on both sides of the x-axis.im not sure about your vertex. i thinks its (9,33)

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  • 1 decade ago

    y = 6+6x-1/3x^2

    3y=18 +18 x - x^2; multiply 3 to make it whole number

    3y -99= -x^2 +18x -81 to make the equation a perfect square

    -3(y+33)=[x-9]^2

    the opening was downward

    V=(9,-33)

    : j

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