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Chapter 11: Q. 11.29 (page 1093)

Graphx=-y2-4y+12by using properties.

Short Answer

Expert verified

The graph for the equation x=-y2-4y+12is,

Step by step solution

01

Step 1 Given equation is,

x=-y2-4y+12.

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

Identify the constants a,b,c.

a=-1,b=-4,c=12.

Since a=-1, the parabola opens leftward.

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

Substitute the known values in the formula.

y=-(-4)2-1=-2

02

Step 2 The vertex is on the  line y=-2.

Substitute y=-2in the given equation.

x=--22-4-2+12=-4+8+12=16

The vertex is,16,-2.

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

0=-y2-4y+12y+6y-2=0y=-6,2

The y- intercepts are,0,-6and 0,2.

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

x=0-0+12x=12

The x-intercepts are, 12,0.

The point 12,0is two units above the line of symmetry. The symmetric point two units below the line of symmetry is 12,-4.

03

Step 3 Plot a graph by using the known values.

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