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Chapter 3: Q 53. (page 156)

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

fx=2x2+12x

Short Answer

Expert verified

The given quadratic equation has a minimum value that is-18.

Step by step solution

01

Step 1. Given information.

The given quadratic equation isfx=2x2+12x.

02

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

Compare the given quadratic function fx=2x2+12xwith fx=ax2+bx+c.

So, a=2,b=12,c=0.

If role="math" localid="1646374369558" a=2>0, the parabola opens up, which means that the function has a minimum value and it is vertex.

Hence, the given quadratic function has a minimum value.

03

Step 3. Determine the minimum value.

The minimum value occurs at x=-b2a.

role="math" x=-122脳2鈰�鈰�b=12,a=2=-3

The required minimum value is:

fx=2x2+12xf-3=2-32+12-3=18-36=-18

04

Step 4. Simplified answer.

Hence, the required minimum value is-18.

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