Chapter 11: Q. 62 (page 1101)

In the following exercises, graph each equation by using properties.
$x = 3 y^{2}$

Short Answer

Expert verified

On graphing the equation we get,

Step by step solution

Step 1. Given information.

Consider the given equation,

$x = 3 y^{2}$

Compare $x = a y^{2} + b y + c$ with the given equation,

$a = 3$

Then the parabola opens to the right.

To find the axis of symmetry, find $y = - \frac{b}{2 a}$ . Then,

$y = - \frac{0}{2 (3)} y = 0$

The vertex is on the line $y = 0$ .

Step 2. Find the vertex point.

Substitute $y = 0$ in the original equation,

localid="1645207023473" $x = 3 {(0)}^{2} x = 0$

Therefore, the vertex is $(0, 0)$ .

Since the vertex is $(0, 0)$ , both the x- and y-intercepts are the point $(0, 0)$ .

Substitute various values of y,

x	y
3	1
12	2

Plot the points symmetric to localid="1645207394384" $(3, 1), (12, 2)$ across the y-axis, the points $(3, - 1), (12, - 2)$ .

Step 3. Graph the equation.

Plot the graph,

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In the following exercises, graph each equation by using properties.
$x = 3 y^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the vertex point.

Step 3. Graph the equation.

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In the following exercises, graph each equation by using properties.x=3y2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the vertex point.

Step 3. Graph the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Statistics

Decision Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using properties.
$x = 3 y^{2}$