# Rectangular Coordinate Systems and Graphs of Equations René, René, he’s our man, If he can’t graph it, Nobody can.(2.1, 2.2)

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Rectangular Coordinate Systems and Graphs of Equations René, René, he’s our man, If he can’t graph it, Nobody can.(2.1, 2.2)

POD (And who the heck is René?) Let’s review. Write up here everything you can share about the x-y coordinate plane.

POD Let’s review. Write up here everything you can share about the x-y coordinate plane. Labeling the axes and intervals. Quadrants. Origin. How to plot a point, using ordered pairs. What else?

Distance formula What is it, and how do we use it?

Distance formula Try it. Find the distance between the points A(-3, 6) and B(5,1).

Distance formula Find the distance between the points A(-3, 6) and B(5,1).

Midpoint formula What is it and how do we use it?

Midpoint formula Try it. Find the midpoint of the line segment connecting the points P 1 (-2, 3) and P 2 (4, -2).

Midpoint formula Try it. Find the midpoint of the line segment connecting the points P 1 (-2, 3) and P 2 (4, -2).

Midpoint formula Try it again. Verify that the distances from the midpoint (1,½) to the endpoints, (-2, 3) and (4, -2), are equal.

Midpoint formula Try it again. Verify that the distances from the midpoint (1,½) to the endpoints, (-2, 3) and (4, -2), are equal.

Another level Now, find an equation for the perpendicular bisector of the line segment connecting the points P 1 (-2, 3) and P 2 (4, -2).

Another level Now, find an equation for the perpendicular bisector of the line segment connecting the points P 1 (-2, 3) and P 2 (4, -2). We know a point on that bisector. How do we determine the slope? What do we plug this information into?

Another level Now, find an equation for the perpendicular bisector of the line segment connecting the points P 1 (-2, 3) and P 2 (4, -2). We know a point on that bisector. (1, ½) How do we determine the slope? It’s the negative reciprocal of the segment. That slope is -5/6. The equation: (y - ½) = 6/5(x – 1)

Let’s graph (put on your red shoes and graph the blues) What do you know about graphs on the coordinate plane?

Let’s graph (put on your red shoes and graph the blues) Graphs as solutions of equations Intercepts (how do we find them?) x-y charts Dependent/independent variables Symmetry– to either axis, the origin (see p. 108) Intersections Functions vs. relations (how does this relate to symmetry?) Domain and range

Symmetry Each table graph one of these equations on CAS, then we’ll look as a class. What are the symmetries for each one?

Symmetry At each table, graph each of the equations on calculators. What are their symmetries? to the origin to the y-axis to the origin to the x-axis– not a function! substituting –y for y leads to the same equation

Symmetry In general: Odd functions: symmetric to the origin f(x) = -f(-x) Even functions: symmetric to the y-axis f(x) = f(-x) Not a function!: symmetric to the x-axis substituting –y for y leads to the same equation

Intersections Estimate the points of intersection for the following graphs. How?

Intersections Estimate the points of intersection for the following graphs. How? We could use algebra (how?), but let’s graph here to find out.

Intersections Start by graphing each equation. We can do this on the 94 or CAS. On the 84, hit 2 nd Calc- intersect.

Intersections You’ll be asked to mark the curves involved. Hit enter one more time to get the final result.

Intersections Finding the intersections on CAS isn’t a whole lot different (You’ll be glad to know we’ll end here, because it’s a short period. Woo-hoo.)

Circles (the wheels on the bus go ‘round and ‘round) Remember what the equation for a circle is?

Circles (the wheels on the bus go ‘round and ‘round) Remember what the equation for a circle is? What do the variables represent? Are we talking functions? Why or why not?

Circles (the wheels on the bus go ‘round and ‘round) Remember what the equation for a circle is? What do the variables represent? (h, k) is the center, r is the radius No function. No VLT.

Circles Use it. Find an equation of the circle with a center C(-2, 3) and containing the point D(4, 5).

Circles Use it. Find an equation of the circle with a center C(-2, 3) and containing the point D(4, 5). Find r with the distance formula.

Circles Use it. Find an equation of the circle with a center C(-2, 3) and containing the point D(4, 5). Find r with the distance formula. Final equation:

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