Point of intersection of two functions

Question

In the $xy$ - plane, the point of intersection of two functions $f(x) = x^2$ and $g(x) = x + 2$ lies in which quadrant/s ?

I have no idea how to begin with this question.

Answer 1

First, let us solve

$$f(x)=g(x)$$

$$x^2=x+2$$

$$0=x^2-x-2$$

By the quadratic formula, we know

$$x=-1\text{ or }x=2$$

Now, for the first solution we get

$$(-1,f(-1))=(-1,1)$$

while for the second we get

$$(2,f(2))=(2,4)$$

Clearly, the first solution is in quadrant $2$ while the second solution is in quadrant $1$. Thus, $f(x)$ and $g(x)$ intersect in quadrants $1$ and $2$.

Answer 2

Go forward like you would mathematically, That is equating the two functions.

$f(x) = g(x)$

$x^2 = x + 2$

$x^2 - x - 2 = 0$

$x = -1$ or $x = 2$

The corresponding points are (-1,1) and (2,4) which lie in $2^{nd}$ and $1^{st}$ quadrant respectively

Answer 3

Hint : We know that $f(x) = x^2 \ge 0$ for all $x$ . In which quadrants would this function lie ?

Also $f(x) = x+2$ is defined in all quadrants except $4^{\text{th}}$ quadrant.

Can you now find the intersection of both the functions ?