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ElenaW [278]
2 years ago
6

Consider the equation y\:=\:-x^2\:-\:7x\:+\:12. Determine whether the function has a maximum or a minimum value. State the maxim

um or minimum value. What are the domain and range of the function?

Mathematics
1 answer:
kondor19780726 [428]2 years ago
6 0

Answer:

Step-by-step 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=\frac{-b}{2a}  and  k=c-\frac{b^2}{4a} (These are derived from the quadratic formula). Filling in knowing our a = -1, b = -7, c = 12:

h=\frac{-(-7)}{2(-1)}=\frac{7}{-2}=-\frac{7}{2}  and

k=12-\frac{(-7)^2}{4(-1)}=12-(\frac{49}{-4})=12+\frac{49}{4}=\frac{97}{4} so the vertex (aka max height occurs at (-\frac{7}{2},\frac{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 | y ≤ 97/4}

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

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