How do you find the domain and range of #M(x)= -2/14x^2-11x-15#?

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Answer 1 · 2017-04-20T16:57:28

Find the Vertex.

This is a quadratic function, whose graph is a parabola.

First, find its vertex, #(h, k)#.

For #y = ax^2 + bx + c#, the #x#-coordinate of the vertex is

#h = -b/(2a.)#

In this case

#h = -11/(2/7) = -11*(7/2) = -77/2#.

#k = M(h) = -(1/7)(-77/2)^2 - 11(-77/2) - 15 = 787/4#

Since #a < 0#, the graph opens down.

The domain of every polynomial function is #(-oo, oo)#.
The range is #(-oo, 787/4]#.