Thursday
April 17, 2014

Homework Help: College Algebra

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)((-2)^2-4(1)(1fx)-3)/(2(1))
x=22 (4-f(x))/2
x=1+(4-f(x)
x=2-2(4-f(x))/2
x=1+(4-f(x), x=1-(4-f(x)
(4-f(x))<0
f(x)>4
=f(x) 4 (-,4] range

domain= all real numbers

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