Question

identify the zeros and y-intercept for the following function.
$y = -(x - 3)^2 - 4$
(there is a graph of a parabola here)
select one:
○ a. zeros = (0,0), y-intercept = none
○ b. zeros = (0,-13), y-intercept = none
○ c. zeros = none, y-intercept = (0, -13).
○ d. zeros = none, y-intercept = none

Explanation:

Step1: Find Zeros (Set \( y = 0 \))

Set \( y = 0 \) in \( y = -(x - 3)^2 - 4 \):
\( 0 = -(x - 3)^2 - 4 \)
\( (x - 3)^2 = -4 \)
Since the square of a real number cannot be negative, there are no real zeros.

Step2: Find y-intercept (Set \( x = 0 \))

Set \( x = 0 \) in \( y = -(x - 3)^2 - 4 \):
\( y = -(0 - 3)^2 - 4 \)
\( y = -9 - 4 = -13 \)
So the y-intercept is \( (0, -13) \).

Answer:

C. zeros = None, y-intercept = (0, -13)