Answer:
Step-by-step explanation:
Number 2 first:
See the graph below for a hint. (Do you know how to use Desmos ?)
factoring seems to make no sense for [tex]y =-x^{2} +2x +4[/tex] but "guess and check" seems to work. I tried 4 for x, but that proved false. 3 for x made sense. You get [tex]-3x^{2} +2(3) +4 =y[/tex] so -9 +6 +4 = 1 is true. So (3,1)
x+y=4 becomes 3 + 1 = 4 Also true
According to the graph, (0,4) would also be a solution, so (3,1) and (0,4)
Part 1:
Factor [tex]x^{2} +4x +3[/tex] as [tex](x + 3)(x + 1)[/tex] set each equal to 0 and get
x = -3 and x = -1 so the solutions seem be (-3,0) and (-1,0)
y = 2x + 6 factors to 2(x +3)
(-1,0) doesn't work!
But Desmos shows something else as a solution set for both:
(1,8)
y=2x+6 substitute values 8=2(1) +6 8=2+6 True
y = [tex]x^{2} +4x +3[/tex]. Substitute values [tex]8 =1^{2} +4(1) +3[/tex] 8= 1+4+3 True
