Question

find all the zeros of the quadratic function.
$y = x^2 + 7x + 12$
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 \( y = x^2 + 7x + 12 \), we set \( y = 0 \), so we have the equation \( x^2 + 7x + 12 = 0 \).

Step2: Factor the quadratic

We factor the quadratic expression. We need two numbers that multiply to \( 12 \) and add up to \( 7 \). The numbers \( 3 \) and \( 4 \) work because \( 3 \times 4 = 12 \) and \( 3 + 4 = 7 \). So, we can factor the quadratic as \( (x + 3)(x + 4) = 0 \).

Step3: Solve for \( x \)

Using the zero - product property, if \( (x + 3)(x + 4)=0 \), then either \( x + 3 = 0 \) or \( x + 4 = 0 \).

• For \( x + 3 = 0 \), subtracting \( 3 \) from both sides gives \( x=-3 \).
• For \( x + 4 = 0 \), subtracting \( 4 \) from both sides gives \( x = - 4 \).

Answer:

-3, -4