Anonymous
Anonymous asked in 科學及數學數學 · 1 decade ago

CE Maths

Given that in the graph of quadratic function f(x)=x^2+bx+c, the line x=1 is the axis of symmetry.

a) find the value of b

Given that (2,0) is a point on the graph

b) find the value of c

c) find the y-coordinate of the vertex of the graph.

d) if the graph of y=f(x) is reflected in the y-axis and enlarged 2 times of the resulting graph along the y-axis, find the y-coordinate of the vertex of the final graph.

1 Answer

Rating
  • 1 decade ago
    Best Answer

    by completing square,

    f(x)

    =x^2+bx+c

    =(x+b/2)^2 - (b^2) /4 + c

    given the line x=1 is the axis of symmetry,

    - b/2 = 1

    b= -2 <-- ans of (a)

    sub (2,0) into y=x^2-2x+c

    c= 0 <-- ans of (b)

    y-coordinate of the vertex of the graph: - (b^2) /4 + c

    sub b=-2 and c= 0,

    therefore, y-coordinate of the vertex of the graph = -1 <-- ans of (c)

    when the graph is reflected in the y-axis,

    f'(x)=(x-1)^2 -1

    enlarged 2 times of the resulting graph along the y-axis,

    f''(x)

    = 2f'(x)

    =2(x-1)^2 -2

    therefore,y-coordinate of the vertex of the final graph = -2 <-- ans of (d)

    2009-01-03 16:30:53 補充:

    sorry, part (d) 正負號打錯... 但答案應該一樣...

    when the graph is reflected in the y-axis,

    f'(x)=(x+1)^2 -1

    enlarged 2 times of the resulting graph along the y-axis,

    f''(x)

    = 2f'(x)

    =2(x+1)^2 -2

    therefore,y-coordinate of the vertex of the final graph = -2 <-- ans of (d)

    Source(s): i hope i'm correct
Still have questions? Get your answers by asking now.