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Chapter 11: Q. 11.30 (page 1093)

Graphx=-y2+2y-3by using properties.

Short Answer

Expert verified

The graph for the function x=-y2+2y-3is,

Step by step solution

01

Step 1 Given equations are,

x=-y2+2y-3.

Compare the given equation with x=ay2+by+c.

Identify the constants a,b,c.

a=-1,b=2,c=-3

Since a=-1, the parabola opens leftward.

To find the axis of symmetry, y=-b2a.

Substitute the known values in the formula.

y=-22-1=1

02

Step 2 The vertex is on the line y=1.

Substitute y=1in the given equation.

x=-12+21-3=-1+2-3=-2

The vertex is, -2,1.

To find the y- intercepts, substitute x=0in the given equation.

0=-y2+2y-3

The solution of this quadratic equation are the complex numbers. So, there are no y- intercepts.

To find x- intercepts, substitute y=0in the given equation.

x=0+0-3x=-3

The x- intercepts are, -3,0.

The point -3,0is one unit below the line of symmetry. The line of symmetry one unit above the line of symmetry is, -3,2.

03

Step 3 Now plot a graph by using the known values.

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Most popular questions from this chapter

For the functionf(x)=25x2-81, find:
(a) the zeros of the function.

(b) the x-intercepts of the graph

of the function.
(c) the y-intercept of the graph of the

function.

In the following exercises, simplify each expression.

y43.y52

Use the Quotient Property to simplify square roots.

(a)50m72m

(b)125023

(c)486y92y34

Simplify:

(a)2723

(b)81-32

(c)16-34

In the following exercises, factor each expression using any method4a2+5a+2
See all solutions

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