Question

To show how to solve the equation, create two functions and find their intersection points. What two functions can be used to solve the following equation, and what is their solution set?

x2+4x−1=2x+2

(1 point)
Responses

f(x)=x2+4x−1, g(x)=2x+2, {−3,1}
f left parenthesis x right parenthesis equals x squared plus 4 x minus 1 , g left parenthesis x right parenthesis equals 2 x plus 2 , left brace negative 3 comma 1 right brace

f(x)=x2+4x, g(x)=2x, {−3,1}
f left parenthesis x right parenthesis equals x squared plus 4 x , g left parenthesis x right parenthesis equals 2 x , left brace negative 3 comma 1 right brace

f(x)=x2+4x−1, g(x)=2x+2, {−3,−4,1,4}
f left parenthesis x right parenthesis equals x squared plus 4 x minus 1 , g left parenthesis x right parenthesis equals 2 x plus 2 , left brace negative 3 comma negative 4 comma 1 comma 4 right brace

f(x)=x2+4x−1, g(x)=2x+2, {−1,3}
f left parenthesis x right parenthesis equals x squared plus 4 x minus 1 , g left parenthesis x right parenthesis equals 2 x plus 2 , left brace negative 1 comma 3 right brace
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Answer 1

To solve the equation x^2 + 4x - 1 = 2x + 2, we can create two functions and find their intersection points.

Let f(x) = x^2 + 4x - 1 and g(x) = 2x + 2.

To find the intersection points, we set f(x) equal to g(x):

x^2 + 4x - 1 = 2x + 2

Bringing all the terms to one side, we have:

x^2 + 2x - 3 = 0

Now we can factor the quadratic equation or use the quadratic formula to find the solutions. In this case, the equation can be factored as:

(x + 3)(x - 1) = 0

Setting each factor equal to zero, we get:

x + 3 = 0 or x - 1 = 0

Solving these equations, we find:

x = -3 or x = 1

Therefore, the solution set to the equation x^2 + 4x - 1 = 2x + 2 is {-3, 1}.