Question

PLEASE HELP ASAP!!!!! THANK YOU~

Answer 1

Answer:

$y=4x^2-8x-4$

Step-by-step explanation:

Quadratic Function

The quadratic function can be expressed in the following form:

$y=a(x-x_1)(x-x_2)$

Where a is a real number different from 0, and x1, x2 are the roots or zeroes of the function.

From the conditions stated in the problem, we know

x_1=1+\sqrt{2}, \ x_1=1-\sqrt{2}

Substitute in the general formula above:

$y=a[x-(1+\sqrt{2})][x-(1-\sqrt{2})]$

Operate the indicated product

$y=a(x^2-2x-1)$

To find the value of a, we use the y-intercept which is the value of y when x=0, thus

$y=a(0^2-2(0)-1)=-4$

It follows that

$a=4$

Thus, the required quadratic function is

$y=4(x^2-2x-1)$

Or, equivalently

$\boxed{y=4x^2-8x-4}$