Question

Consider the equation y\:=\:-x^2\:-\:7x\:+\:12. Determine whether the function has a maximum or a minimum value. State the maximum or minimum value. What are the domain and range of the function?

Answer 1

Explanation:

To answer this we need only know that negative parabolas are upside down, so by definition, it has a max point at the vertex. To find the vertex (h, k), the easy way to do this is to fill in the following expressions for h and k and solve:

`h=(-b)/(2a)` and
`k=c-(b^2)/(4a)` (These are derived from the quadratic formula). Filling in knowing our a = -1, b = -7, c = 12:

`h=(-(-7))/(2(-1))=(7)/(-2)=-(7)/(2)` and

`k=12-((-7)^2)/(4(-1))=12-((49)/(-4))=12+(49)/(4)=(97)/(4)` so the vertex (aka max height occurs at
`(-(7)/(2),(97)/(4))`. Depending upon what is meant by stating the max value, we may only need to state the k value (which is the same as the y coordinate, which is an up or down thing as opposed to the x value which is a side to side thing). The domain is all real numbers, as is the case for all x-squared parabolas, and the range is

R = y ≤ 97/4

I can't see your choices so match them up from these answers to the ones in the list of choices.