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Pearson Algebra 2 Common Core, 2011 View details

10. Normal Distributions

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Exercise 41 Page 745

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

Graph:

Conic Section: circle with center (0,0) and radius 8
Lines of Symmetry: all lines through the center
Domain: - 8 ≤ x ≤ 8
Range: - 8 ≤ y ≤ 8

Practice makes perfect

To begin with, we have to rewrite our polynomial equation in its standard form. x^2+y^2=64 To graph the given equation, we now have to make a table of values.

x	x^2+y^2=64	y
- 6	( - 6)^2+y^2=64	≈ ± 5.3
- 4	( - 4)^2+y^2=64	≈ ± 6.9
0	( 0)^2+y^2=64	± 8
4	( 4)^2+y^2=64	≈ ± 6.9
6	( 6)^2+y^2=64	≈ ± 5.3

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 circle with radius 8 and a center at (0,0).
The x-intercepts are ( - 8,0 ) and ( 8,0 ).
The y-intercepts are ( 0,- 8 ) and ( 0,8 ).
Every line through the center is a line of symmetry, so there are infinitely many lines of symmetry.
The domain is the set of real numbers x such that - 8 ≤ x ≤ 8.
The range is the set of real numbers y such that - 8 ≤ y ≤ 8.

Subchapter links

Lesson Check p.743

Practice and Problem-Solving Exercises p.743-745

Standardized Test Prep p.745

Mixed Review p.745

Exercise 41 Page 745

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