Chapter 10: Q 65. (page 655)

Graph each function.
$f (x) = \sqrt{16 - 4 x^{2}}$ .

Short Answer

Expert verified

The graph of the function is half an ellipse.

Step by step solution

Step 1. Given information.

We have given function $y = \sqrt{16 - 4 x^{2}}$

Now, find equation of conic in a standard form we have

role="math" localid="1646757247233" $y^{2} = {(\sqrt{16 - 4 x^{2}})}^{2} y^{2} = 16 - 4 x^{2} y^{2} + 4 x^{2} = 16 \frac{y^{2}}{16} + \frac{4 x^{2}}{16} = \frac{16}{16} \frac{y^{2}}{16} + \frac{x^{2}}{4} = 1 \frac{x^{2}}{2^{2}} + \frac{y^{2}}{4^{2}} = 1$

Step 2. Graph of the function.

Substitute $b = 2$ and $a = 4$ in $b^{2} = a^{2} - c^{2}$ .

$c^{2} = 4^{2} - 2^{2} c^{2} = 12 c = \sqrt{12} c = 2 \sqrt{3}$

The foci at $(0, \pm 2 \sqrt{3})$ .

The vertices of the major axis of the ellipse are at $(0, 4)$ and $(0, - 4)$ .

The vertices of the minor axis of the ellipse are at $(2, 0)$ and $(- 2, 0)$ .

Use the vertices and foci of the ellipse to graph the function is

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Graph each function.
$f (x) = \sqrt{16 - 4 x^{2}}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph of the function.

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Graph each function.f(x)=16-4x2.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Decision Maths

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Geometry

Study anywhere. Anytime. Across all devices.

Graph each function.
$f (x) = \sqrt{16 - 4 x^{2}}$ .