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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)

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

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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?

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

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

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

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

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

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

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

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

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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).

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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?

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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)

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

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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

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

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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

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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

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

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

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

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

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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.)

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

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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?

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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.

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

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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.

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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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