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Chapter 11: Q.77 (page 1101)

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

x=-3(y-2)2+3

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=-3(y-2)2+3

The graph of the parabola is to be determined

02

Step 2. Equation of the parabola

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

The given equation isx=-3(y-2)2+3

Herea=-3,k=2,h=3

Since a is negative, the parabola opens to the left.

03

Step 3. Axis of symmetry

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

Plugging the values:

y=2

Hence the axis of symmetry isy=2

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(3,2)

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=-3(y-2)2+3x=-3(0-2)2+3x=-3(-2)2+3x=-3(4)+3x=-12+3x=-9

Hence the x-intercept is (-9,0)


y-intercept:

Plugging x=0in the equation:

role="math" localid="1645431300485" x=-3(y-2)2+30=-3(y-2)2+3-3(y-2)2=-33(y-2)2=3(y-2)2=1y-2=卤1y-2=卤1y=卤1+2y=1+2,y=-1+2y=3,y=1


Hence y-intercepts are (0,3),(0,1)

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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