Question

Jackie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?


f(x) g(x)
graph of the function f of x equals one half times x squared, plus 1
x g(x)
1 −1
2 −2
3 −3
Yes, at positive x-coordinates
Yes, at negative x-coordinates
Yes, at negative and positive x-coordinates
No, they will not intersect

Answer 1

They will not intersect.

Answer 2

Answer:

No, they will not intersect

Step-by-step explanation:

We are given a expression of the function f(x) as:

$f(x)=\dfrac{1}{2}x^2+1$

and the table of values for g(x) is given as:

x g(x)

1 −1

2 −2

3 −3

i.e. the function is given as:

$g(x)=-x$

Also we can find the equation of g(x) by the slope intercept form i.e. $y=mx+c$

Here $y=g(x)$

When x=1 y=-1

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

And when x=2 y=-2

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

On solving the above two equations i.e. eqn(1) and (2) by method of elimination we have:

m=-1 and c=0

Hence $y=g(x)=-x$

From the graph of f(x) and g(x) we could clearly see that the graph of two functions do not intersect at any point in the coordinate plane.

Hence, last option is correct.

No, they will not intersect