Graph the functions on the same coordinate plane. f(x)=7 g(x)=x2+2x−8 What are the solutions to the equation f(x)=g(x)?

Question

−5

−3

3

5

7

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Answer 1 · 2018-04-11T13:56:02

#x = -5, x = 3#

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the graph in blue is #g(x)#, where #g(x) = x^2+2x-8#
the graph in red is #f(x)#, where #f(x) = 7#.

the points where the two graphs meet are #(-5, 7)# and #(3, 7)#.

at the point #(-5,7):#

#(x,y) = (-5,7)#

#x = -5, y = 7#

#x^2+2x - 8 = 25 - 10 - 8#

# = 15 - 8 #

#= 7#

hence, #f(x) = 7# when #x = -5#

at the point #(3,7):#

#(x,y) = (3,7)#

#x = 3, y = 7#

#x^2+2x - 8 = 9 + 6 - 8#

# = 15 - 8 #

#= 7#

hence, #f(x) = 7# when #x = 3#

#g(x)# is defined as #7#, so the #y#-coordinate cannot change; for any value of #x#, #y = 7#.

when #x = 3# and when #x = -5#, #f(x) = g(x) = 7#.