Chapter 10: Q 67. (page 655)

Graph each function.
$f (x) = - \sqrt{64 - 16 x^{2}}$

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 is $y = - \sqrt{64 - 16 x^{2}}$ .

Now, find an equation of conic, we have

$y^{2} = 64 - 16 x^{2} y^{2} + 16 x^{2} = 64 \frac{y^{2}}{64} + \frac{x^{2}}{4} = 1 \frac{x^{2}}{2^{2}} + \frac{y^{2}}{8^{2}} = 1$

Step 2. Graph of the function.

We have $b = 2, a = 8$ in $b^{2} = a^{2} - c^{2}$

$c^{2} = 8^{2} - 2^{2} c^{2} = 60 c = \sqrt{60} c = 2 \sqrt{15}$

The foci are at $(0, \pm 2 \sqrt{15})$ .

The vertices of the major axis of the ellipse are at $(0, 8)$ and $(0, - 8)$ .

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

The graph of the function is

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Graph each function.
$f (x) = - \sqrt{64 - 16 x^{2}}$

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)=-64-16x2

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

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Graph each function.
$f (x) = - \sqrt{64 - 16 x^{2}}$