2. For x^2 + y^2 = 4x x = y^2 a. Put the first equation...

2. For \begin{cases} x^2 + y^2 = 4x \\ x = y^2 \end{cases} a. Put the first equation in standard form by completing the square: b. Graph both equations (think about what type of shape it is, find x and y-intercepts, vertex, center, make a table, etc.) c. Based on your graphs, how many solutions will the system have? d. Solve the system using wither substitution or elimination. Make sure to write answers as coordinate points.

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Transcript

00:02 Okay, what we're going to do is graph the system and then solve the system algebraically and find the points of intersection.

00:09 So what we have here is the equation of a circle and that circle is going to have center zero zero and radius two.

00:20 And then we're going to have the equation of a line and that line is going to have slope one and y intercept negative two.

00:28 So we can go ahead and graph those.

00:30 Seems like it would be good to have a scale where each square is half a unit.

00:36 So we'll make a scale on the axes.

00:44 And then for the circle, let's go ahead and put the center in place at zero zero.

00:49 And then from there we want to go up to and down to, right two, and left two.

00:55 And we get our circle.

00:59 Then for the line, we have a y intercept of negative two, so we can put that point in place and a slope of one.

01:05 So we can go up one over one, up one over one, and we get our line.

01:11 So now we have a rough idea of where the points of intersection are.

01:15 So let's go ahead and solve for them algebraically.

01:19 So here's our system again.

01:20 And what we can do is we can substitute and we can put x minus 2 and for y.

01:25 So that gives us x squared plus the quantity x minus 2 squared equals 4...

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