math

A parabola f intersect the x-
axis at B and C and the y-axis at
E.The axis of symmetry of the
parabola has equation x=3.The line
through E and C has equation g(x)=x/2-7/2. Calculate the x coordinate of B

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  1. Since the axis of symmetry is x=3 and the y-intercept is E, the parabola is

    f(x) = a(x-3)^2 + E

    since E is the y-intercept of the parabola, E = -7/2

    f(x) = a(x-3)^2 - 7/2

    Now you know that (7,0) is on the parabola, so

    a(7-3)^2 - 7/2 = 0
    16a = 7/2
    a = 7/32

    f(x) = 7/32 (x-3)^2 - 7/2
    or, since you now know that the roots are at x= 7 and -1 (why?)
    f(x) = 7/32 (x-7)(x+1)

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