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3 votes
What is the minimum value of the function g(x) = x2 - 6x – 12?

-21
3-21
3
3+21

User Chronikum
by
5.9k points

1 Answer

5 votes

Answer:

- 21

Explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

= (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

User Lazlow
by
5.7k points