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Chapter 3: Q. 50 (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-2)2+3or f(x)=-x2+4x-1.

Step by step solution

01

Step 1. Given information.

The given graph is:

02

Step 2. Determine the equation.

The vertex is (2,3), so h=2and k=3. Substitute these values into equation f(x)=a(x-h)2+k.

f(x)=a(x-2)2+3

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

-1=a(0-2)2+3-1-3=4a-4=4a-1=a

Substitute a=-1in f(x)=a(x-2)2+3.

f(x)=-1(x-2)2+3f(x)=-(x-2)2+3f(x)=-x2+4x-4+3f(x)=-x2+4x-1

03

Step 3. Conclusion.

The quadratic function whose graph is given isf(x)=-(x-2)2+3or f(x)=-x2+4x-1.

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Most popular questions from this chapter

If f(x)=x2-4, findf(-2).

The x-coordinate of the vertex of f(x)=ax2+bx+c,a≠0, is ________.

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

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)=x2-6x-1

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)=2x2-4x+1
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