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

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

Step-by-step explanation:

We have the functions,

f of x equals one half times x squared, plus 2 i.e. 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 , we get,

i.e.

i.e.

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).

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step-by-step explanation: