Question

Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed? Check all that apply.

g(x) = x2 – 4x – 21
g(x) = (x – 3)(x + 7)
g(x) = 3x2 – 12x – 63
g(x) = –(x + 3)(x – 7)
g(x) = x2 + 4x – 21

Answer 1

1

3

4

Explanation:

Answer 2

• g(x) = x^2 – 4x – 21
• g(x) = 3x^2 – 12x – 63
• g(x) = –(x + 3)(x – 7)

Explanation:

When r is an x-intercept of the function, (x -r) is a factor. The two given x-intercepts mean that two factors of the function are (x -(-3))(x -7). There may be a vertical scale factor that is not necessarily positive.

These factors multiply out to give ...

(x +3)(x -7) = x^2 -4x -21 . . . . . . matches the first choice

When this expression is multiplied by 3, it matches the third choice:

3(x +3)(x -7) = 3x^2 -12x -63

When the factored form is multiplied by -1, it matches the fourth choice:

-(x +3)(x -7)