Question

find all the zeros of the quadratic function. y = x² - 8x - 9 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 \( y = x^2 - 8x - 9 \), we set \( y = 0 \), so we have the equation \( x^2 - 8x - 9 = 0 \).

Step2: Factor the quadratic

We factor the quadratic expression. We need two numbers that multiply to \( -9 \) and add up to \( -8 \). The numbers are \( -9 \) and \( 1 \). So, \( x^2 - 8x - 9=(x - 9)(x + 1)=0 \).

Step3: Solve for \( x \)

Using the zero - product property, if \( (x - 9)(x + 1)=0 \), then either \( x - 9 = 0 \) or \( x + 1 = 0 \).

• If \( x - 9 = 0 \), then \( x=9 \).
• If \( x + 1 = 0 \), then \( x=-1 \).

Answer:

\( 9, - 1 \)