Answer :
To determine the correct statement about the function [tex]\( y = x^2 - 3x - 40 \)[/tex], we need to find the zeros of the function. Zeros of a function, also known as roots, are the values of [tex]\(x\)[/tex] for which [tex]\( y = 0 \)[/tex].
We have been provided with the result that the zeros of this equation are [tex]\(-5\)[/tex] and [tex]\(8\)[/tex]. These values are the solutions to the equation [tex]\( x^2 - 3x - 40 = 0 \)[/tex].
Let’s verify which statement accurately describes the zeros and the factored form of the equation:
1. If [tex]\(-5\)[/tex] and [tex]\(8\)[/tex] are the zeros, the equation can be factored as [tex]\( y = (x + 5)(x - 8) \)[/tex].
2. To verify this, we can expand the factors:
[tex]\[ y = (x + 5)(x - 8) \][/tex]
[tex]\[ y = x^2 - 8x + 5x - 40 \][/tex]
[tex]\[ y = x^2 - 3x - 40 \][/tex]
This matches the given equation [tex]\( y = x^2 - 3x - 40 \)[/tex].
Therefore, statement B: "The zeros are -5 and 8, because [tex]\( y = (x + 5)(x - 8) \)[/tex]" is true.
We have been provided with the result that the zeros of this equation are [tex]\(-5\)[/tex] and [tex]\(8\)[/tex]. These values are the solutions to the equation [tex]\( x^2 - 3x - 40 = 0 \)[/tex].
Let’s verify which statement accurately describes the zeros and the factored form of the equation:
1. If [tex]\(-5\)[/tex] and [tex]\(8\)[/tex] are the zeros, the equation can be factored as [tex]\( y = (x + 5)(x - 8) \)[/tex].
2. To verify this, we can expand the factors:
[tex]\[ y = (x + 5)(x - 8) \][/tex]
[tex]\[ y = x^2 - 8x + 5x - 40 \][/tex]
[tex]\[ y = x^2 - 3x - 40 \][/tex]
This matches the given equation [tex]\( y = x^2 - 3x - 40 \)[/tex].
Therefore, statement B: "The zeros are -5 and 8, because [tex]\( y = (x + 5)(x - 8) \)[/tex]" is true.
