Question

find all the zeros of the quadratic function.
$y = x^2 + 16x + 64$
if there is more than one zero, separate them with commas.
if there are no zeros, click on
one\.
zero(s):

Explanation:

Step1: Factor the quadratic

The quadratic \( y = x^2 + 16x + 64 \) is a perfect square trinomial. We know that \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, \( a = x \), \( 2ab = 16x \), so \( 2b = 16 \) implies \( b = 8 \), and \( b^2 = 64 \). So, \( x^2 + 16x + 64=(x + 8)^2 \).

Step2: Find the zeros

To find the zeros, set \( y = 0 \), so \( (x + 8)^2 = 0 \). Taking the square root of both sides, we get \( x + 8 = 0 \), which gives \( x=-8 \). Since the square of a number is zero only when the number itself is zero, this is a repeated root.

Answer:

-8