Chapter 11: Q. 11.27 (page 1092)

Graph $x = y^{2}$ by using properties.

Short Answer

Expert verified

The graph for the function $x = y^{2}$ is ,

Step by step solution

Step 1 Given equation is,

$x = y^{2}$ .

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

we get, $a = 1$ .

Since $a = 1$ , the parabola opens rightward.

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

So, $y = 0$ .

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

Step 2 Substitute y=0 in the given equation.

$x = 0$ .

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

Since the vertex is $(0, 0)$ , both the $x$ - and $y$ -intercepts are the point $(0, 0)$ . To graph the parabola we need more points.

Let us draw a table to choose values of $y$ .

Step 3 Now find the symmetric points.

The points symmetric to $(1, 1)$ and $(4, 2)$ across the $y$ - axis are, $(1, - 1)$ and $(4, - 2)$ .

Now plot the graph for the given function by using the known values.

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Graph $x = y^{2}$ by using properties.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Substitute y=0 in the given equation.

Step 3 Now find the symmetric points.

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Graph x=y2by using properties.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Substitute y=0 in the given equation.

Step 3 Now find the symmetric points.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Graph $x = y^{2}$ by using properties.