Question

Type the correct answer in each box. use numerals instead of words. the function y = x4 ? 16x2 has zeros at x = -4, x = 0, and x = , and a y-intercept at (0,).

Answer 1

Explanation:

The function y = x^4 - 16x^2 has zeros at x = -4, x = 0, and x = 4, and a y-intercept at (0, 0).

To find the zeros of a function, we set the function equal to zero and solve for x. In this case, we have:

x^4 - 16x^2 = 0

Factoring out common terms, we get:

x^2(x^2 - 16) = 0

Now we can use the zero product property which states that if the product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for x:

x^2 = 0 => x = 0

x^2 - 16 = 0 => x^2 = 16 => x = ±√16

Simplifying, we have:

x = -4, x = 0, and x = 4

Therefore, the function has zeros at x = -4, x = 0, and x = 4.

To find the y-intercept, we substitute x = 0 into the function:

y = (0)^4 - 16(0)^2 = 0

So, the y-intercept is (0, 0).

In summary:

- The function y = x^4 - 16x^2 has zeros at x = -4, x = 0, and x = 4.

- The y-intercept is at the point (0, 0).