Question

find all the zeros of the quadratic function.
$y = x^2 + 15x + 36$
if there is more than one zero, separate them with commas.
if there are no zeros, click on
one\.
zero(s):

Explanation:

Step1: Set \( y = 0 \)

To find the zeros of the quadratic function \( y = x^2 + 15x + 36 \), we set \( y = 0 \), so we have the equation \( x^2 + 15x + 36 = 0 \).

Step2: Factor the quadratic

We need to factor the quadratic expression. We look for two numbers that multiply to \( 36 \) (the constant term) and add up to \( 15 \) (the coefficient of \( x \)). The numbers \( 12 \) and \( 3 \) work because \( 12 \times 3 = 36 \) and \( 12 + 3 = 15 \). So we can factor the quadratic as \( (x + 3)(x + 12) = 0 \).

Step3: Solve for \( x \)

Using the zero - product property, if \( (x + 3)(x + 12)=0 \), then either \( x + 3 = 0 \) or \( x + 12 = 0 \).

• For \( x + 3 = 0 \), subtracting \( 3 \) from both sides gives \( x=-3 \).
• For \( x + 12 = 0 \), subtracting \( 12 \) from both sides gives \( x = - 12 \).

Answer:

-12, -3