Question

which equation matches the x - intercepts x = 5, -7?

1. ( y=(x - 5)(x - 7) )
2. ( y=(x + 5)(x - 7) )
3. ( y=(x + 5)(x + 7) )
4. ( y=(x - 5)(x + 7) )

Explanation:

Step1: Recall x - intercept formula

For a quadratic (or polynomial) function, if \( x = a \) is an x - intercept, then \( (x - a) \) is a factor of the function.

Step2: Determine factors from x - intercepts

Given x - intercepts \( x = 5 \) and \( x=-7 \).

• For \( x = 5 \), the factor is \( (x - 5) \) (since \( x-5 = 0\) when \( x = 5 \)).
• For \( x=-7 \), the factor is \( (x+7) \) (since \( x + 7=0\) when \( x=-7 \)).

So the function should be \( y=(x - 5)(x + 7) \).

Answer:

1. \( y=(x - 5)(x + 7) \)