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

$x = -5, x = 3$

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

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 $x = -5$ , $f(x) = g(x) = 7$ .