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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 43 Page 745

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

Graph:

Conic Section: ellipse centered at (0,0) with foci at (±4,0)
Lines of Symmetry: x=0 and y=0
Domain: - 5 ≤ x ≤ 5
Range: - 3 ≤ y ≤ 3

Practice makes perfect

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

x	9x^2+25y^2=225	y
- 5	9( - 5)^2+25y^2=225	0
- 3	9( - 3)^2+25y^2=225	± 2.4
0	9( 0)^2+25y^2=225	± 3
3	9( 3)^2+25y^2=225	± 2.4
5	9( 5)^2+25y^2=225	0

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 an ellipse centered at (0,0) and has foci at (±4,0).
The x-intercepts are (- 5,0) and (5,0).
The y-intercepts are ( 0,3 ) and ( 0,3 ).
The ellipse has two lines of symmetry, x=0 and y=0.
The domain is the set of real numbers x such that - 5 ≤ x ≤ 5.
The range is the set of real numbers y such that - 3 ≤ y ≤ 3.

Extra

Calculating foci

Each ellipse has two foci. We calculate them by using the following formula, with x being the point where the ellipse intersects the x-axis and y being the point where the ellipse intersects the y-axis. (± sqrt(y^2-x^2),0) We have that x= ± 3 and y= ± 5. We can substitute the values into the formula and calculate the foci location.

(± sqrt(y^2-x^2),0)

x= ± 3, y= ± 5

(± sqrt(( ± 5)^2-( ± 3)^2),0)

Calculate power

(± sqrt(25-9),0)

Subtract term

(± sqrt(16),0)

Calculate root

(± 4,0)

Subchapter links

Lesson Check p.743

Practice and Problem-Solving Exercises p.743-745

Standardized Test Prep p.745

Mixed Review p.745