# Which of the graphs below correctly solves for x in the equation x2 − 4x + 3 = x + 3?

Which of the graphs below correctly solves for x in the equation x2 − 4x + 3 = x + 3?

the question does not present the options, but this does not interfere with the resolution

let
f(x)=x² − 4x + 3
g(x)=x + 3

we know that
the solution for
f(x)=g(x)

is the intersection both graphs

using a graph tool
see the attached figure

the solution are the points
(0,3)  and (5,8) (0,3) (5,8) is the correct answer

(-3,-1) and (1,-5)

Step-by-step explanation:

Given : Let f(x)= Let g(x)= Plot these graphs using graphical tool .

The intersection point of these two equations will be the solution .

Refer the attached graph.

Thus the intersection points are (-3,-1) and (1,-5)

So, the solution is (-3,-1) and (1,-5)

Thus the graph which gives the correct solution is attached below. B

Step-by-step explanation:

Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5

Step-by-step explanation:

we have we can separate the expression above into two equations ----> equation A

This is a quadratic equation ( vertical parabola) open downward (the leading coefficient is negative) ----> equation B

This is a linear equation with negative slope (decreasing function).so linear sloping up to the left

The solution of the original expression are the x-coordinates of the intersection point both graphs

using a graphing tool

The intersection points are (-3,-1) and (1,-5)

see the attached figure Step-by-step explanation:

(-2,-8)

(4,10)

The second graph opening downward with the points (-3, -9) and (3, 9)

Step-by-step explanation:

x=1 or x=-3 ilike

Step-by-step explanation:

subtract -x-4 from both sides and left side of equation and the last step is set factor equal to 0

I also get (0;5). What are the options?
I'm assuming the answer choices are A through D, and they are sorted from left to right (A being left-most; D being right-most)

Choice A can be eliminated since the line has a negative slope. The slope for y = 2x+5 is positive (positive 2).

Choice B can be eliminated since the y intercept here is negative. The y intercept is 5 for y = 2x+5

Choice D can be eliminated because the parabola should open downward (the negative leading coefficient tells us this)

Choice C is the only choice left. Therefore it is the final answer.

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