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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

10. Normal Distributions

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Exercise 42 Page 745

Make a table of values, plot the obtained points, and connect them with a smooth curve.

Graph:

Conic Section: hyperbola, centered at (0,0)
Foci: (± 3sqrt(2),0)
Lines of Symmetry: x=0 and y=0
Domain: x ≤ - 3 or x ≥ 3
Range: All real numbers

Practice makes perfect

To graph the given equation, we will make a table of values.

x	x^2-y^2=9	y
- 5	( - 5)^2-y^2=9	± 4
- 4	( - 4)^2-y^2=9	≈ ± 2.6
- 3	( - 3)^2-y^2=9	0
- 2	( - 2)^2-y^2=9	-
- 1	( - 1)^2-y^2=9	-
0	0^2-y^2=9	-
1	1^2-y^2=9	-
2	2^2-y^2=9	-
3	3^2-y^2=9	0
4	4^2-y^2=9	≈ ± 2.6
5	5^2-y^2=9	± 4

We will now plot and connect the obtained points with a smooth curve.

Let's describe what we see in this graph.

The conic section is a hyperbola that consists of two branches, and is centered at (0,0).
The x-intercepts are (- 3,0) and (3,0).
There are no y-intercepts.
The hyperbola has two lines of symmetry, x=0 and y=0.
The domain is the set of real numbers x such that x ≤ - 3 or x ≥ 3.
The range is the set of all real numbers.

Subchapter links

Lesson Check p.743

Practice and Problem-Solving Exercises p.743-745

Standardized Test Prep p.745

Mixed Review p.745