The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola

Question

The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?

y = (x – 2)(x + 3)
y = (x – 2)(x + 3)
y = (x + 2)(x – 3)
y = (x + 2)(x – 3)

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Huyền Thanh 5 months 2021-09-05T09:05:08+00:00 1 Answers 3 views 0

Answers ( )

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    2021-09-05T09:06:14+00:00

    Answer:

    y =-\frac{1}{2}(x +2)(x - 3)

    Step-by-step explanation:

    Given

    x_1 = -2

    x_2 = 3

    (x,y) = (-1,2) — a point on the parabola

    Required

    The equation

    First, calculate the equation from the zeros

    y =k(x - x_1)(x - x_2)

    Substitute x_1 = -2 and x_2 = 3

    y =k(x - -2)(x - 3)

    y =k(x +2)(x - 3)

    To solve for k, we substitute (x,y) = (-1,2)

    2 = k(-1+2)(-1-3)

    2 = k(1)(-4)

    2 = -4k

    Divide by -4

    k=\frac{2}{-4}

    k=-\frac{1}{2}

    So, the equation is:

    y =k(x +2)(x - 3)

    y =-\frac{1}{2}(x +2)(x - 3)

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )