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The curve has the equation y = 2x(3−x). It crosses the x-axis at O and B. A straight line crosses the y-axis at B with coordinates (0,5). Find the equation of the line.

Mathematics

ScanSolve AI Answer

Graph of y = 2x(3 − x)

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Key points of y = 2x(3 − x)
Pointxy
x-intercept00
Maximum1.54.5
x-intercept30

Step-by-step solution

2 steps

  1. Identify the coordinates of point B.

    The curve has the equation y=2x(3−x)y = 2x(3-x). It crosses the x-axis at O and B.
    To find the x-intercepts, set y=0y=0:

    2x(3−x)=02x(3-x) = 0

    This gives x=0x=0 or 3−x=0⇒x=33-x=0 \Rightarrow x=3.
    Since O is the origin (0,0)(0,0), point B must be the other x-intercept.
    The coordinates of point B are (3,0)(3,0).

  2. Interpret the information about the straight line and point D.

    The problem states: "A straight line, which crosses the y-axis at the point B with coordinates $(0,5

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