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Chapter 3: Q. 6 (page 175)

Determine the quadratic function for the given graph.

Short Answer

Expert verified

The quadratic function isf(x)=2(x-1)2-32.

Step by step solution

01

Step 1. Given information.

Determine the quadratic function for the given graph.

02

Step 2. Find the quadratic function.

If the vertex h,kand one point on the graph of a quadratic function are known, then we can write

f(x)=a(x-h)2+k

From the given graph, vertex is 1,-32so,h=1andk=-32

Now substitute these values into the equation

f(x)=a(x-h)2+k

To determine the value of a, use a fact that point5,0 is on the graph.

03

Step 3. substitute the values.

f(5)=a5-12-320=16a-3216a=32a=2

Substitute the value of ainto the function.

f(x)=a(x-h)2+k=2(x-1)2-32

04

Step 4. Conclusion. 

The quadratic function isf(x)=2(x-1)2-32.

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Most popular questions from this chapter

Match each graph to one the following functions.

f(x)=x2-2x+1

To complete the square of x2-5x, you add the number _______.

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+4x+2

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)
-2-26
-1-4
02
1-2
2-10

List the intercepts of the equation y=x2-9.
See all solutions

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