On a piece of paper, graph the system of equations. y=x-2 y=x^2-6x+8

ANSWER

Option C.

EXPLANATION

The first equation is

We can easily graph this straight line because it has a slope of 1 and a y-intercept of -2.

The second equation is

This is a graph of a quadratic function. If we write this in vertex form, we can easily graph it using transformations.

We complete the square to get the function to the vertex form as follows:

This quadratic graph has its minimum point (vertex) at (3,-1).

To find the point of intersection of the two graphs, we equate the two functions and solve for x.

We rewrite in standard form

Factor to obtain

The solutions are

When x=2, y=2-2=0

This gives (2,0) as a point of intersection.

When x=5, y=5-2=3.

This gives us (5,3) as another point of intersection.

The correct answer is option C.