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Chapter 3: Q 59. (page 156)

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

fx=-3x2+12x+1

Short Answer

Expert verified

The maximum value is13.

Step by step solution

01

Step 1. Given information.

The given function isfx=-3x2+12x+1.

02

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

Compare the given function fx=-3x2+12x+1with fx=ax2+bx+c.

So, a=-3,b=12,c=1.

If a=-3<0, then 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.

role="math" localid="1646460944766" x=-122-3=126=2

The required maximum value is:

fx=-3x2+12x+1f2=-322+122+1=-12+24+1=13

04

Step 4. Simplified answer.

Hence, the required maximum value is13.

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