How do you find the range of the equation #y = -x^2 – 6x – 13#?

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Answer 1 · 2017-08-18T13:20:32

Range of #y = [-4,-oo)#

#y = -x^2-6x-13#

#y# is a quadratic function, represented on the #xy-#plane as a parabola of the form: #ax^2+bx+c#

The vertex of the parabola will be at #x=( -b)/(2a)#

In our case, #b=-6, a=-1#

Hence, #x_(vertex) = (6)/(-2) =-3#

Since #a<0# then #y(x_(vertex) )# will be a maximum of #y#

#:. y_max = y(-3) = -(-3)^2+6*3-13 = -9+18-13=-4#

#:. # the greatest value of #y# is #-4#

Since #y# has no lower bounds, the range of #y# is #[-4, -oo)#

As can be seen from the graph of #y# below.

graph{-x^2-6x-13 [-23.18, 22.45, -15.1, 7.71]}