Question

Determine the factored form equation of a quadratic with zeros of x=√2 and x=-√2 and passing through the point (2,−4).

(a) (x+√2)(x−√2)-4
(b) (x+√2)(x−√2)+4
(c) (2x+√2)(2x-√2)-4
(d) (2x+√2)(2x-√2)+4

Answer 1

The factored form equation of the quadratic with zeros of x=√2 and x=-√2 and passing through the point (2,−4) is (d) (2x + √2)(2x - √2) + 4.

Step-by-step explanation:

To determine the factored form equation of a quadratic with zeros of x=√2 and x=-√2 and passing through the point (2,−4), we can use the zero-product property. The factored form of the quadratic equation is given by (x - √2)(x + √2), as the zeros are the opposite of the square root values. To find the equation with the given point, we substitute the values of x and y into the factored form equation:

(2 - √2)(2 + √2) = -4

Simplifying further, we get:

(4 - 2) = -4

The equation simplifies to:

2 = -4

Since the equation is not true, the correct factored form equation is (d) (2x + √2)(2x - √2) + 4.