Question

Mary is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? Which coordinates if they do? Negative or positive or both?

Answer 1

they will not intersect

Answer 2

The graphs of the two function will not intersect.

Explanation:

We are given a quadratic function f(x).

Also g(x) is given by a set of values as:

x g(x)

1 -1

2 0

3 1

As g(x) is a linear function hence we find out the equation of g(x) by the slope intercept form of a line: y=mx+c

let g(x)=y

when x=1 , g(x)=-1

-1=m+c----(1)

when x=2 , g(x)=0

0=2m+c------(2)

Hence, on solving (1) and (2) by method of elimination we get:

m=1 and c=-2

Hence, the equation of g(x) is:

g(x)=x-2

So clearly from the graph we could see that the graph of the two functions will never intersect.