Question

Nellie 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 2
x g(x)
1 5
2 10
3 15

Answer 1

Yes, the functions intersects at the points (0,2) and (9.583,47.913).

Explanation:

We have the functions,

f of x equals one half times x squared, plus 2 i.e.
`f(x)=(x^(2))/(2)+2` and g(x) given by the table.

The general form of a linear function is y=mx+b, where m is the slope and b is the y-intercept.

We will find the slope of the function g(x),

Using
`slope=(y_(2)-y_(1))/(x_(2)-x_(1))`, we get,

i.e.
`m=(10-5)/(2-1)`

i.e.
`m=\frac{5}1}`

i.e. m= 5.

So, substituting (1,5) in y=5x+b ⇒ 5 = 5×1+b ⇒ b= 0.

Thus, the equation of g(x) is y= 5x.

After plotting the function f(x) and g(x), we get the following graph.

From the graph, we see that, the functions intersects at the points (0,2) and (9.583,47.913).