Complete the square to determine the maximum or minimum value of the function defined by the expression.

−x^2 − 6x + 6

a) minimum value at 3
b) maximum value at 15
c) minimum value at −1
d) minimum value at −6

Option B - Maximum value at 15

Step-by-step explanation:

Given : Expression

To find : Complete the square to determine the maximum or minimum value of the function defined by the expression?

Solution :

Step 1 - Write quadratic function in standard or vertex form.

The vertex form

Applying completing the square into

Step 2 - Determine the direction of the graph.

If the parabola opens upward, we will be finding its minimum value.

If the parabola opens downward, we will find its maximum value.

It depends on the value of a

a=-1 i.e. negative so the parabola opens downward we will find its maximum value.

Step 3 - The maximum value attain at point k

(h,k) are the vertex of the parabola on comparing we get,

k=15

So, The Expression has maximum value at 15.

Therefore, Option B is correct.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.