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Gelneren [198K]
4 years ago
6

Let ​ f(x)=x2+14x+36 ​ .

Mathematics
1 answer:
azamat4 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

The vertex form of f(x) is

f(x) = (x - h)² + k

where (h, k) are the coordinates of the vertex

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 14x

f(x) = x² + 2(7)x + 49 - 49 + 36

     = (x + 7)² - 13

The minimum value of f(x) is the y- coordinate of the vertex

vertex = (- 7, - 13), that is minimum value = - 13

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