Chapter 10: Q. 53 (page 644)

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
$x^{2} - 4 x = y + 4$

Short Answer

Expert verified

The vertex is $(2, - 8)$ , focus is $(2, \frac{- 31}{4})$ and the directrix is $y = \frac{- 33}{4}$ .

The graph of the equation shown below .

Step by step solution

Step 1. Given information .

Consider the given equation $x^{2} - 4 x = y + 4$ .

Step 2. Analyze the equation .

The standard form of the parabola is ${(x - h)}^{2} = 4 a (y - k)$ .

Compare the given equation with standard form .

role="math" localid="1647088607109" ${(x - h)}^{2} = 4 a (y - k) {(x - 2)}^{2} = (y + 8) a = \frac{1}{4} h = 2, k = - 8$

Further simplify .

Since the value of $a = \frac{1}{4}$ the vertex is $(h, k) = (2, - 8)$ and focus $(h, k + a) = (2, \frac{- 31}{4})$ and the directrix is $y = \frac{- 33}{4}$ .

Step 3. Plot the graph .

The graph of the equation $x^{2} - 4 x = y + 4$ using graphing utility is shown below .

Here V is the vertex , F is focus and the line $y = \frac{- 33}{4}$ represents the directrix of the parabola .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
$x^{2} - 4 x = y + 4$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Analyze the equation .

Step 3. Plot the graph .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.x2-4x=y+4

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Analyze the equation .

Step 3. Plot the graph .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
$x^{2} - 4 x = y + 4$