Factor the binomial completely. x2−81

(x - 9)(x + 9)

Step-by-step explanation:

x² - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), then

x² - 81

= x² - 9²

= (x - 9)(x + 9)

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1