Finding the
Roots/Zeros

  x = {-√7, √7, -i, i}

Step-by-step explanation:

The quartic can be factored as the product of two quadratics:

  f(x) = x^4 -6x^2 -7

  f(x) = (x^2 -7)(x^2 +1)

Each quadratic can be factored according to the factoring of the difference of squares:

  x^2 -a^2 = (x -a)(x +a)

Of course, the square root of a negative number is imaginary. The full factorization is then ...

  f(x) = (x -√7)(x +√7)(x -i)(x +i)

The zeros are ...

  x = {-√7, √7, -i, i}

lo98765432wqasdfghjkloi87654567890

step-by-step explanation:

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.