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Chapter 3: Q. 4 (page 155)

To graph y=(x-4)2, you shift the graph of y=x2to the ______ a distance of ______ units.

Short Answer

Expert verified

Shift the graph ofy=x2to the right a distance of 4 units.

Step by step solution

01

Step 1. Given information.

The given equations are:

y=x-42y=x2

02

Step 2. Determine the type of shift.

If the argument xof a function fis replaced by x-h,h>0, the graph of the new function y=f(x-h)is the graph of fshifted horizontally right hunits.

The function y=x-42is in the form of y=fx-h, whereh=4. It means the graph ofy=x2shifts 4 units to the right.

03

Step 3. Conclusion.

Shift the graph ofy=x2 to the right a distance of4 units.

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Most popular questions from this chapter

On one set of coordinate axes, graph the family of parabolas f(x)=x2+bx+1for b = -4, b = 0, and b = 4. Describe the general characteristics of this family.

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=23x2+43x-1

Determine the quadratic function whose graph is given.

If h(x)=-23x+4,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.

Find an equation of the line containing the points (1,4)and (3,8).
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