Question

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

Answer 1

I believe the first answer is correct.

Answer 2

Option (1) is correct.

They will intersect at positive x coordinate.

Explanation:

Given : A graph for function f(x)

We have to check weather function f(x) and g(x) intersect or not.

We first determine the function g(x)

Given :

1) x= 1 then g(x) = 5

2) x = 2 then g(x) = 10

Equation of line is given as g(x) = mx + c

Where , m is slope and c is the point where line touches y axis.

Slope
`m=(y_2-y_1)/(x_2-x_1)`

Substitute,

`m=(10-5)/(2-1)=5`

Substitute we get

y = 5x + c

For c substitute x = 1 y = 5 we get c = 0

Thus g(x) = 5x

Now we plot it on the graph to see whether they intersect or not.

From graph attached below

They will intersect at positive x coordinate.

Option (1) is correct.