Answer:
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
The minimum value of the function is 4.
The minimum value of the function is the lowest possible value it can reach.
It is given that: f(x) = x² + 10x + 29
The given function has a minimum value since the coefficient of the first term is not negative.
We can find the minimum value by completeig the square.
f(x) = x^2 + 10x + 29
⇒f(x) = x² + 2(5)x + (5)² - (5)² + 29
⇒f(x) = (x + 5)² - 25 + 29
⇒f(x) = (x + 5)² + 4
Now we can make the square term zero by substituting x =-5
f(-5) = (-5 + 5)² + 4
= 4
This is the minimum value of f(x).
Therefore, we have found the minimum value of the function as 4.
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