If lylah completes the square for f(x)=x^2-12x+7 in order to find the minimum, she must write f(x) in the general form f(x)=(x-a)^2+b. what is the value of a for f(x)?

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Step-by-step explanation:

We have been given that Lylah completes the square for . In order to find the minimum she must write f(x) in the general form .

We know that vertex form of a parabola is in format , where, (h,k) is the vertex of parabola.

To complete the square for given equation, we will set our given equation equals 0.

Now, we will add to both sides of our given equation.

Upon comparing our equation by vertex form of parabola, we can see that the vertex of parabola is at point . Therefore, the value of 'a' for f(x) is 6.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0