Let f (x) = x^2+10x+29 .

What is the minimum value of the function?

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The minimum value of the function is 4

4

Step-by-step explanation:

given

f (x) = x² + 10x + 29

Since the coefficient of the x² term > 0, f (x) will have a minimum value

Use the method of completing the square

add / subtract (half the coefficient of the x - term) ² to x² + 10x

f (x) = x² + 2 ( + 5) x + (5) ² - (5) ² + 29

= (x + 5) ² - 25 + 29

= (x + 5) ² + 4

When x = - 5, f (x) has a minimum value at + 4