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Chapter 3: Q. 47 (page 156)

Determine the quadratic function whose graph is given.

Short Answer

Expert verified

The quadratic function whose graph is given is f(x)=(x+1)2-2or f(x)=x2+2x-1.

Step by step solution

01

Step 1. Given information.

The given graph is:

02

Step 2. Determine the equation.

The vertex is (-1,-2), so h=-1and k=-2. Substitute these values into equation f(x)=a(x-h)2+k.

f(x)=a(x-(-1))2+(-2)f(x)=a(x+1)2-2

To determine the value of a, we use the fact that f(0)=-1(the y-intercept).

-1=a(0+1)2-2-1+2=a1=a

Substitute a=1in f(x)=a(x+1)2-2.

localid="1646122557882" f(x)=1(x+1)2-2f(x)=(x+1)2-2f(x)=x2+2x+1-2f(x)=x2+2x-1

03

Step 3. Conclusion.

The quadratic function whose graph is given is f(x)=(x+1)2-2or f(x)=x2+2x-1.

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Most popular questions from this chapter

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

xy=f(x)
-2-8
-1-3
00
11
20

Match each graph to one the following functions.

f(x)=x2-2x+1

If p(x)=-x+6,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.

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.

Show that the inequality (x-4)2≤0has exactly one solution.
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