If f(x) = x2 − 6x + 19, complete the square and determine the minimum or maximum value of the function

minimum value = 10

Step-by-step explanation:

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 using completing the square

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

f(x) = x² + 2(- 3)x + 9 - 9 + 19

     = (x - 3)² + 10 ← in vertex form

with (h, k) = (3, 10 )

To determine maximum or minimum consider the value of a

• If a > 0 then minimum value of k

• If a < 0 then maximum value of k

Here a = 1 > 0, hence minimum value of k = 10

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step-by-step explanation:

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.