Jacques needs to convert the function f(x) = x2 − 6x + 14 to vertex form, f(x) = (x − h)2 + k, in order to find the minimum. when he does this, what is the value of k in the vertex form of function f? a. 23 b. 9 c. 5 d. 14

k = 5

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

Since the coefficient of the x² term is 1 then

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

f(x) = x² + 2(- 3)x + 9 - 9 + 14 = (x - 3)² + 5 → k = 5

C. 5

Step-by-step explanation:

Given function is,

Here, the coefficient of x = 6,

Thus, We need to add and subtract the square of half of 6 in the given equation for getting the vertex form,

By adding and subtracting 9,

  ( Because, a² - 2ab + b² = (a-b)²  )

Which is the required vertex form he will get,

By comparing it with

We get, k = 5,

⇒ Option C is correct.

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

part a: 1.08

part b: 27.59