Posted by **Sunny** on Wednesday, January 4, 2012 at 5:43pm.

Here is the whole question... I have figured most of it out but I need help with part (b)(f) and (g)... Maybe you also check the work I have already done

Given the following function, find:

(a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range,

(f) intervals where the function is increasing,

(g) intervals where the function is decreasing, and

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

here's my work

y=-x^2+2x+3

y=-1(x^2-2x+1)-1(-3)-(-1)(0+1)

y=1(x^2-2x+1)-1(-3)-(-1)(1)

y=-1(x-1)^2-1(-3)-(-1)(1)

y=-1(x-1)^2+3-(-1)(1)

y=-1(x-1)^2+3+1

y=-1(x-1)^2+4

y=a(x-h)^2+k

a=-1 k=4 h=1

Vetex=(1,4)

axis of symmetry=

(0)=-x^2+2x+3

-x^2+2x+3=0

x^2-2x-3=0

(x+1)(x-3)=0

x=-1,3

y=-(0)^2+2(0)+3

y=-(0)+2(0)+3

y=0+0+3

y=3

-x^2+2x-f(x)=0

-x^2*-1+2x*-1+3*-f(x)*-1=0*-1

x^2-2x+f(x)-3=0*-1

x^2-2x+f(x)-3=0

a=1 b=-2 c= 1f(x)-3

x=-(2)¡À¡Ì((-2)^2-4(1)(1fx)-3)/(2(1))

x=2¡À2 ¡Ì(4-f(x))/2

x=1+¡Ì(4-f(x)

x=2-2¡Ì(4-f(x))/2

x=1+¡Ì(4-f(x), x=1-¡Ì(4-f(x)

(4-f(x))<0

f(x)>4

=f(x)¡Ü 4 (-¡Þ,4] range

domain= all real numbers

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