Chapter 8: Q39. (page 424)

Write an equation for each parabola described below. Then draw the graph.
39. vertex (1, 7), directrix y = 3.

Short Answer

Expert verified

The equation of the parabola is $y = 2 {(x - 1)}^{2} + 7$ .

The graph is:

Step by step solution

Step 1. Given

Vertex (1, 7), directrix $y = 3$ .

Step 2. To determine

Write an equation for the parabola. Then draw the graph.

Step 3. Calculation

Since the directrix is parallel to the x-axis, so the standard form of the parabola is:

$y = a {(x - h)}^{2} + k$

Vertex = $(h, k) = (1, 7)$

$\begin{matrix} 2 a = Distance between vertex and directrix \\ = 7 - 3 \\ = 4 \end{matrix}$

So, $a = 2$

So, the equation becomes:

$\begin{matrix} y = a {(x - h)}^{2} + k \\ y = 2 {(x - 1)}^{2} + 7 \end{matrix}$

Using a graphing calculator, the graph is:

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Write an equation for each parabola described below. Then draw the graph.
39. vertex (1, 7), directrix y = 3.

Short Answer

Step by step solution

Step 1. Given

Step 2. To determine

Step 3. Calculation

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Write an equation for each parabola described below. Then draw the graph.39. vertex (1, 7), directrix y = 3.

Short Answer

Step by step solution

Step 1. Given

Step 2. To determine

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Discrete Mathematics

Calculus

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Write an equation for each parabola described below. Then draw the graph.
39. vertex (1, 7), directrix y = 3.