Chapter 10: Q. 54 (page 644)

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
$y^{2} + 12 y = - x + 1$

Short Answer

Expert verified

The vertex is $(37, - 6)$ and the directrix is $x = \frac{149}{4}$ .

The graph for the equation shown below .

Step by step solution

Step 1. Given information .

Consider the give equation $y^{2} + 12 y = - x + 1$ .

Step 2. Analyze the equation .

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

Compare the given equation with standard form .

${(y - k)}^{2} = 4 a (x - h) {(y + 6)}^{2} = - x + 37 a = \frac{- 1}{4} h = 37, k = - 6$

Further simplify .

Since $a = \frac{- 1}{4}$ the vertex is $(37, - 6)$ and the directrix is $x = \frac{149}{4}$ .

Step 3. Plot the graph .

The graph of the equation $y^{2} + 12 y = - x + 1$ using graphing utility is shown below .

Here V is the vertex , and the line $x = \frac{149}{4}$ represents the directrix of the parabola .

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Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
$y^{2} + 12 y = - x + 1$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Analyze the equation .

Step 3. Plot the graph .

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Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.y2+12y=-x+1

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

Calculus

Mechanics Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

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.
$y^{2} + 12 y = - x + 1$