Question

Based on the graph below, what is the solution of the equation f(x) = g(x)? graph of function f of x equals negative x plus 0.25 and graph of function g of x equals x squared plus 3 multiplied by x plus 2

A) x = −3.5 and x = −0.5
B) x = −2 and x = −1
C) x = −3.5 and x = 0.25
D) x = −2 and x = 0.25

Just need to check, no explanation needed.

Answer 1

hello :
f(x) = -x+0.25
g(x) = x²+3x+2
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f(-3.5) = 3.75

g(-3.5) = 3.75


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f(-0.5) =0.75
g(-0.5) = 0.75
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conclusion : answer : A) x = −3.5 and x = −0.5

Answer 2

The answer is the option A

`x=-3.5\ and\ x=-0.5`

Explanation:

we have

`f(x)=-x+0.25` ------> equation A

`g(x)=x^(2) +3x+2` -----> equation B

`f(x)=g(x)`

`-x+0.25=x^(2) +3x+2`

`x^(2) +3x+2+x-0.25=0`

`x^(2) +4x+1.75=0`

Find the x-intercepts of the quadratic equation

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2) +4x=-1.75`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2)+4x+4=-1.75+4`

`x^(2)+4x+4=2.25`

Rewrite as perfect squares

`(x+2)^(2)=2.25`

Square root both sides

`x+2=(+/-)1.5`

`x=-2(+/-)1.5`

`x=-2+1.5=-0.5`

`x=-2-1.5=-3.5`