Answer
Intersection points: $(\displaystyle \frac{1-\sqrt{5}}{2},\frac{3-\sqrt{5}}{2})$ and $(\displaystyle \frac{1+\sqrt{5}}{2},\frac{3+\sqrt{5}}{2})$
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Work Step by Step
See attached image (desmos.com).
To find the intersection points algebraically,
substitute $y=1+x $ into the second equation:
$(1+x)=x^{2}$
$0=x^{2}-x-1$
$x=\displaystyle \frac{-(-1)\pm\sqrt{1-4(1)(-1)}}{2(1)}$
$ x=\displaystyle \frac{1\pm\sqrt{5}}{2}\qquad$... $ \displaystyle \frac{1+\sqrt{5}}{2}\approx 1.618,\quad \frac{1-\sqrt{5}}{2}\approx-0.618,$
Back-substitute:
$x=\displaystyle \frac{1+\sqrt{5}}{2}\quad \Rightarrow\quad y= \frac{1+\sqrt{5}}{2}+1=\frac{3+\sqrt{5}}{2}\approx 2.618$
$x=\displaystyle \frac{1-\sqrt{5}}{2}\quad \Rightarrow\quad y= \frac{1-\sqrt{5}}{2}+1=\frac{3-\sqrt{5}}{2}\approx 0.382$
Intersection points: $(\displaystyle \frac{1-\sqrt{5}}{2},\frac{3-\sqrt{5}}{2})$ and $(\displaystyle \frac{1+\sqrt{5}}{2},\frac{3+\sqrt{5}}{2})$
