Question

compare the properties of the two functions problem.determine if the functions have a min or a max values and if their zeros are real or complex

Answer 1

Hello:)

and what are the functions?

Answer 2

f(x)=25-2x-x^2 and g(x)=x^2-2x-25

Answer 3

\(\color{#000000}{ \displaystyle f(x)=-x^2-2x+25 }\)
\(\color{#000000}{ \displaystyle g(x)=x^2-2x-25 }\)

I will re-write them that way.

Answer 4

Well, g(x) has an \(x^2\) term in there.
That means that the bigger the x gets (in this case, bigger=magnitude)
the larger the output would get.

Is there a limit to how large g(x) is going to get? (If there is, then, what)

Answer 5

no sir dosent say a limit

Answer 6

The bigger the x gets, the higher up will g(x) go.
It will boundlessly go up. That means g(x) has no maximum.

Answer 7

Although, g(x) would have a minimum.
At the vertex.

Answer 8

The rule is that if the parabola opens up (has a positive coefficient of x^2 term), then the minimum is the vertex, and no maximum.

The rule is that if the parabola opens down (has a negative coefficient of x^2 term), then the maximum is the vertex, and no minimum.

Answer 9

So, a function in a form:
\(\color{#000000}{ \displaystyle h(x)= ax^2-bx+c }\)

Will have, Minimum at the vertex.
No Maximum.


And a function in a form:
\(\color{#000000}{ \displaystyle h(x)= -ax^2-bx+c }\)

Will have, Maximum at the vertex.
No Minimum.

Answer 10

And to find the zeros, you will set each function =0, and solve for x.