Question

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

Answer 1

ANSWER

Option C.

EXPLANATION

The first equation is

$y = x - 2$

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

The second equation is

$y = {x}^{2} - 6x + 8$

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:

$y = {x}^{2} - 6x +9 + 8 - 9$

$y = (x { - 3)}^{2} - 1$

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

Points of intersection

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

${x}^{2} - 6x + 8 = x - 2$

We rewrite in standard form

${x}^{2} - 7x + 10 = 0$

Factor to obtain

$(x - 2)(x - 5) = 0$

The solutions are

$x = 2 \: and \: x = 5$

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.

Answer 2

Answer: C

Step-by-step explanation: graph both equations and see where they intersect. Use desmos.com/calculator