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Chapter 3: Q 57. (page 156)

Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.

fx=-x2+10x-4

Short Answer

Expert verified

The maximum value is21.

Step by step solution

01

Step 1. Given information.

The given equation is fx=-x2+10x-4.

02

Step 2. Determine whether the graph of the function opens up or down.

Compare the given quadratic function fx=-x2+10x-4with fx=ax2+bx+c.

So, here a=-1,b=10,c=-4.

If a=-1<0, the parabola opens down, which means that the function has a maximum value and it is the vertex.

03

Step 3. Determine the minimum value.

The maximum value occurs at x=-b2a.

x=-102-1=102=5

The maximum value is:

fx=-x2+10x-4=-52+105-4=-25+50-4=25-4=21

04

Step 4. Simplified answer.

Hence, the required maximum value is21.

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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.

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