please help.
find the range of $$f(x)=x ^{2}-6x+2$$

Question

please help.
find the range of $$f(x)=x ^{2}-6x+2$$

anonymous · Answer

This is parabola opened up. So find vertex.
$$f(x)=x ^{2}-6x+7+2-7=(x-3)^{2}-7$$
so vertex is at (3,-7)
so range is (-7, infinity)

anonymous · Answer

See if you can simplify the quadratic and linear terms. Then find a constant from them that yields 2. This will help you find the vertex of the parabola and thus the range. Take note of how the parabola opens.

anonymous · Answer

thank you. what was the formula to find the vertex?

anonymous · Answer

You can see that when x is 3, the quadratic term is 0. This is the minima for the function. So the function is at a minimum when x = 3. Note that it is also shifted down 7 units.

anonymous · Answer

Since the parabola opens up (an even polynomial which is not negated) the function will only grow from the vertex also.

anonymous · Answer

to find vertex of a parabola put it in this form:
$$y=a(x-h)^{2}+k$$
vertex will be at (h,k)

anonymous · Answer

ok thank you i just did it myself and i understand it!

anonymous · Answer

good job, glad to help