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Chapter 11: Q.79 (page 1101)

In the following exercises, graph each equation by using properties.

x=4(y+1)2-4

Short Answer

Expert verified

The graph of the equation is

Step by step solution

01

Step 1. Given Information

Given equation of the parabola isx=4(y+1)2-4

The graph of the parabola is to be determined

02

Step 2. Equation of the parabola

The equation of a parabola in standard form x=a(y-k)2+h

The given equation is x=4(y+1)2-4

Here a=4,k=-1,h=-4

Since a is positive, the parabola opens to the right.

03

Step 3. Axis of symmetry

The axis of symmetry of the parabola x=a(y-k)2+hisy=k

Plugging the values:

y=-1

Hence the axis of symmetry isy=-1

04

Step 4. Vertex of a parabola

The vertex of the parabola x=a(y-k)2+his(h,k)

The vertex of the given parabola is(-4,-1)

05

Step 5. Intercepts

x-intercept is the point where the graph crosses the x-axis and y is 0.

y-intercept is the point where the graph crosses the y-axis and x is 0.

x-intercept:

Plugging y=0in the equation:

x=4(y+1)2-4x=4(0+1)2-4x=4(1)2-4x=4-4x=0

Hence the x-intercept is(0,0)


y-intercept:

Plugging x=0in the equation:

localid="1645433676926" x=4(y+1)2-40=4(y+1)2-44(y+1)2=4(y+1)2=1y+1=卤1y=卤1-1y=卤1-1y=1-1,y=-1-1y=0,y=-2

Hence the y-intercepts arelocalid="1645536930764" (0,0),(0,-2)

06

Step 6. Graphing the parabola

Using the properties, plotting the points and graphing the parabola:

07

Conclusion 

The graph of the parabola is

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