Answer:
Yes they will intersect.
Step-by-step explanation:
Given : Neil is analyzing a quadratic function f(x) and a linear function g(x).
and
x -1 -3 -5
g(x) 0 1 2
To find : Will they intersect?
Solution :
Given Points for g(x) are (-1,0) , (-3,1) and (-5,2).
As g is a linear function,
Then it must be in form of g(x) = mx +c
where, c is constant and m is slope.
Using slope formula,
Here,
The equation form is
Now, Put (-5,2) point as it also satisfy the equation
The the equation of g(x) is
Now, We plot the equation of f(x) and g(x) in graphing tool.
The function is plotted by red curve.
The function is plotted by blue curve.
The intersection point of both the curve is (-3,1) and (-1.5,0.25).
Therefore, Yes the function intersect.
Refer the attached figure below.