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)?

−5

−3

3

5

7

1 Answer
LM
Apr 11, 2018

x=−5,x=3

Explanation:

![desmos.com/calculator](useruploads.socratic.org)

the graph in blue is g(x), where g(x)=x2+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

x2+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

x2+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.

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