Question

which function has zeros at \\(x = -2\\) and \\(x = 5\\)?

\\(f(x) = x^2 - 3x - 10\\)

\\(f(x) = x^2 + 3x - 10\\)

\\(f(x) = x^2 + 2x - 10\\)

Explanation:

Identify the given zeros

$$ x_1 = -2,\quad x_2 = 5 $$

Write the factored form of the quadratic function

$$ f(x) = (x - x_1)(x - x_2) = (x - (-2))(x - 5) = (x + 2)(x - 5) $$

Expand the factored expression

$$ f(x) = x^2 - 5x + 2x - 10 = x^2 - 3x - 10 $$

Answer:

• (A) \(f(x) = x^2 - 3x - 10\) (Correct answer)
• (B) \(f(x) = x^2 + 3x - 10\)
• (C) \(f(x) = x^2 + 2x - 10\)