Chapter 11: Q. 11.28 (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 leftward.

To find the axis of symmetry, $y = \frac{- b}{2 a} y = 0 .$

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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Graphx=-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

Statistics

Discrete Mathematics

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Geometry

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Calculus

Study anywhere. Anytime. Across all devices.

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