Question

Given the equations of a straight line f(x) (in slope-intercept form) and a parabola g(x) (in standard form), describe how to determine the number of intersection points, without finding the coordinates of such points. Do not give an example.

Answer 1

Answer:

Step-by-step explanation:

Hello, when you try to find the intersection point(s) you need to solve a system like this one

$\begin{cases} y&= m * x + p }\\ y &= a*x^2 +b*x+c }\end{cases}$

So, you come up with a polynomial equation like.

$ax^2+bx+c=mx+p\\\\ax^2+(b-m)x+c-p=0$

And then, we can estimate the discriminant.

$\Delta=(b-m)^2-4*a*(c-p)$

If $\Delta$ there is no real solution, no intersection point.

If $\Delta=0$ there is one intersection point.

If $\Delta>0$ there are two real solutions, so two intersection points.

Hope this helps.