Question

Please help ASPA

Graph the functions on the same coordinate axis.

f(x)=-2x+1
g(x)=x²-2x-3

What are the solutions to the system of equations?

Select each correct answer.
(-2, -3)
(-2,5)
(2, -3)
(2,5)
(2, 3)

Answer 1

Answer: (2,-3) and (-2,5)

Explanation:

Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1

Hence the slope of the line is -2 and the y intercept is 1.

Hence one point through which it is passing is (0,1) .
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line 2.

It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ; ; (-1,0)iii) x=2 ; ;(2,-3)iii) x=1 ; ;(1,-4)iii) x=-2 ; ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.