SOLUTION: I am having trouble with this problem... Quadratic: y=x^2-6x+8 1). what are the x-intercepts? 2). what is the domain? 3). what is the range? thank you so much for your hel

Algebra ->  Functions -> SOLUTION: I am having trouble with this problem... Quadratic: y=x^2-6x+8 1). what are the x-intercepts? 2). what is the domain? 3). what is the range? thank you so much for your hel      Log On


   

Question 1159347: I am having trouble with this problem...
Quadratic: y=x^2-6x+8
1). what are the x-intercepts?
2). what is the domain?
3). what is the range?
thank you so much for your help
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y is greater than or equal to -1, for range.
x can be any real value, for domain.

x%5E2-6x%2B8=0
%28x-2%29%28x-4%29=0
x-intercepts at 2 and 4.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Quadratic:
y=x%5E2-6x%2B8......factor
y=x%5E2-2x-4x%2B8
y=%28x%5E2-2x%29-%284x-8%29
y=x%28x-2%29-4%28x-2%29
y=%28x-4%29%28x-2%29

1). what are the x-intercepts?
set y=0
0=%28x-4%29%28x-2%29
if %28x-4%29=0->x=4
if %28x-2%29=0->x=2
the x-intercepts are: x=2 and x=4

2). what is the domain?
R (all real numbers) (it's parabola)

3). what is the range?
since it's parabola that opens up, it's vertex is a minimum and range is all real numbers above y-coordinate of the vertex
so, rewrite equation in vertex form
y=x%5E2-6x%2B8.......complete square
y=%28x%5E2-6x%29%2B8
y=%28x%5E2-6x%2Bb%5E2%29-b%5E2%2B8......b=6%2F2=3
y=%28x%5E2-6x%2B3%5E2%29-3%5E2%2B8
y=%28x-3%29%5E2-9%2B8
y=%28x-3%29%5E2-1-> h=3 and k=-1-> vertex is at (3,-1)
so, the range is:
{ y element R : y%3E=-1 }