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The graph shows the graph of y = 3−2x−x2 passing through A, B and C. Find the coordinates of A, B and C.

Mathematics

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Answer

(-3, 0)
(0, 3)
(1, 0)
Graph of y = 3 − 2x − x²

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Key points of y = 3 − 2x − x²
Pointxy
x-intercept−30
Maximum−14
y-intercept03
x-intercept10

Step-by-step solution

2 steps

I understand you're having trouble with the image clarity, besa. I've done my best to decipher the question from the combined images. It appears to be asking for the coordinates of points A, B, and C on the graph of the equation y=3−2x−x2y = 3 - 2x - x^2.

  1. Find the coordinates of B (y-intercept).

    The y-intercept occurs when x=0x = 0. Substitute x=0x = 0 into the equation:

    y=3−2(0)−(0)2y = 3 - 2(0) - (0)^2 y=3−0−0y = 3 - 0 - 0 y=3y = 3

    So, the coordinates of B are (0,3)(0, 3).

  2. Find the coordinates of A and C (x-intercepts).

    The x-intercepts occur when y=0y = 0. Set y=0y = 0 in the equation and solve for xx:

    0=3−2x−x20 = 3 - 2x - x^2

    Rearrange the equation to a standard quadratic form:

    x2+2x−3=0x^2 + 2x - 3 = 0

    Factorize the quadratic equation:

    (x+3)(x−1)=0(x + 3)(x - 1) = 0

    This gives two possible values for xx:

    x+3=0  ⟹  x=−3x + 3 = 0 \implies x = -3 x−1=0  ⟹  x=1x - 1 = 0 \implies x = 1

    From the sketch, point A is on the negative x-axis and point C is on the positive x-axis.
    So, the coordinates of A are (−3,0)(-3, 0) and the coordinates of C are (1,0)(1, 0).

    The coordinates are:
    A: (−3,0)\boxed{(-3, 0)}
    B: (0,3)\boxed{(0, 3)}
    C: (1,0)\boxed{(1, 0)}

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