Question

Which represents the solution(s) of the system of equations, y = x^2 - 6x + 8 and y = -x + 4? Determine the solution set by graphing
(1,3) only
(2,0) and (4,0)
(1, 3) and (4,0)
no solutions

Answer 1

Answer:

(1, 3) and (4,0)

Step-by-step explanation:

The quadratic function is $y=x^2-6x+8$

We can rewrite in the form $y=(x-3)^2-1$

The graph is obtained by shifting the parent quadratic function 3 units right and 1 unit down to obtain the parabola shown in the attachment.

The straight line also have equation $y=-x+4$

The slope is -1 and y-intercept is 4.

We can easily graph this straight line on the same graph as shown in the attachment.

The two graphs intersected at (4,0) and (1,3).

The solution set is therefore  {(x,y)|x=4,y=0 or x=1,y=3}