line through 3,0 and 7,0 and curve at 5,4

Question

Which equation has the same zeros as the function graphed?

(1 point)
Responses

−(x+3)(x+7)=y
negative open paren x plus 3 close paren times open paren x plus 7 close paren is equal to y

(x+3)(x + 7)=y
(x+3)(x + 7)=y

(x−7)2=(x−3)2+y
open paren x minus 7 close paren squared is equal to open paren x minus 3 close paren squared plus y

−(x−3)(x−7)= y

Answer 1

To find which equation has the same zeros as the given function, we first need to identify the zeros from the points mentioned in the problem.

The line through (3,0) and (7,0) indicates that the zeros of the function are \( x = 3 \) and \( x = 7 \). This means the factors of the function will be \( (x - 3) \) and \( (x - 7) \).

Among the options given:

1. −(x + 3)(x + 7) = y: This has zeros at \( x = -3 \) and \( x = -7 \).
2. (x + 3)(x + 7) = y: This has zeros at \( x = -3 \) and \( x = -7 \).
3. (x−7)² = (x−3)² + y: This does not provide clear zeros in the context given.
4. −(x−3)(x−7) = y: This has zeros at \( x = 3 \) and \( x = 7 \).

The correct choice that has the same zeros as the function graphed is:

−(x−3)(x−7) = y.