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Chapter 6: Q12. (page 291)

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=4x2+12x+9

Short Answer

Expert verified

The minimum value of function is 0.

Step by step solution

01

Step 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a鈮�0, the x-coordinate of vertex is -b2a

The graph of f(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
02

Step 2. Given Information.

The given function is f(x)=4x2+12x+9

03

Step 3. Solution.

In the function f(x)=4x2+12x+9, we have

Here, a=4>0

So, the graph opens up and has a minimum value.

The minimum value of the function is the y-coordinate of the vertex.

Thex-coordinate of the vertex is

鈭�b2a=鈭�(12)2(4)..........a=4,b=12=鈭�1.5

Find they-coordinate of the vertex by evaluating the function for x=-1.5.

f(-1.5)=4-1.52+12-1.5+9=0

So, the minimum value of function is 0.

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