Anonymous

# 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.

Rating

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