Question

Solve:f(x) = 2x - 13g(x)= x^2 - 6x + 3

Answer 1

We have the following two functions:

`\begin{gathered} f(x)=2x-13 \\ \\ g(x)=x^2-6x+3 \end{gathered}`

And we need to find a point where the two functions intersect, which results in the solution for the given situation.

To solve this, we can graph both functions, and we need to determine the point at which both functions intersect. That will be the solution we need to find. Then we can use a graphing calculator to graph both functions as follows:

1. Graph the linear function f(x) = 2x -13

We can use the x- and the y-intercepts to graph the line. To find those intercepts, we first need to set y = 0 in the linear function to find the x-intercept (6.5, 0), and then we have to set x = 0 to find the y-intercept of the line (0, -13). Then we ended up with a linear function like the one we have above.

2. Graph the quadratic function.

To graph this, we can see that the function will be a parabola with a minimum. We need to find the vertex (3, -6), and both x-intercepts (0.551,0) and (5.449, 0), the y-intercept (0,3) to graph it as follows:

3. Now we can graph both graphs at the same time, and we have:

We can conclude that both graphs of the corresponding functions intersect at the point (4, -5), or x = 4, and y = -5.

Therefore, the solution to this situation is:

Answer (4, -5)